Question 1

A local charity has decided to solicit donations door-to-door. The table below shows estimated donations for each hour a volunteer spends in the city, in the suburbs, and on campus.

$\begin{array}{cccc}
&&\text { Total Donations fiom: }\
\text { Number of Hours } & \text { The city } & \text { The suburbs } & \text { Campus } \
\hline 1 & \$ 75 & \$ 65 & \$ 45 \
2 & 147 & 127 & 87 \
3 & 215 & 185 & 125 \
4 & 279 & 239 & 159 \
5 & 337 & 289 & 189 \
6 & 380 & 333 & 200
\end{array}$
-With 10 hours of soliciting, the maximum possible amount of donations is

Accepted Answer

The answer of  
A local charity has decided to...

Question 2

A package delivery service currently has 12 vans and 16 employees. Vans cost $400 per week and employees earn $300 per week. The last van added 480 packages delivered to total output, while the last employee added 450 packages. The firm

Accepted Answer

Option C indicates that for the last dollar spent, fewer vans and more employees would be more effective. This is because the firm can deliver more packages per dollar spent on employees than on vans (1.5 vs 1.2 packages delivered).
Option D suggests that the firm could deliver more packages for the same budget by using fewer vans and more employees. This is because, for the same amount of money, the firm can hire more employees than vans (as each van costs $400 while each employee costs $300 per week) resulting in more packages being delivered.
Therefore, options C and D both suggest using fewer vans and more employees to improve delivery output, hence the correct answer is E.

Question 3

Your firm sells club soda in both grocery stores and convenience stores. You have a budget of $550 for store displays, and must decide how to allocate this budget between grocery stores and convenience stores to maximize the total number of sales. The following table shows the total number of units that can be sold in grocery stores and convenience stores, according to the number of displays in each type of store. Displays in grocery stores cost $150 each and displays in convenience stores cost $100 each.

$\begin{array}{cccc}
&&\text {  number of }\
\text { Number of } & \text { Total number of } & \text { displays in } & \text { Total number of } \
\text { displays in } & \text { units sold in } & \text { convenience } & \text { units sold in } \
\text { grocery stores } & \text { grocery stores } & \text { stores } & \text { convenience stores }\\hline 1 & 500 & l & 400 \
2 & 900 & 2 & 780 \
3 & 1,250 & 3 & 1,130 \
4 & 1,550 & 4 & 1,460 \
5 & 1,750 & 5 & 1,760 \
6 & 1,850 & 6 & 1.960
\end{array}$
-Given a budget of $550, the maximum possible number of sales is

Accepted Answer

The answer of  
Your firm sells club soda in...

Question 4

$\begin{array}{cccccc} \text { Level of } & \text { Total } & \text { Total } & \text { Marginal } & \text { Marginal } & \text { Net } \ \text { Activit } & \text { Beneft } & \text { Cost } & \text { Benefit } & \text { Cost } & \text { Benefit }\\hline 0&-&0&xx&xx&0\1&200&30&-&-&-\2&-&-&100&-&230\3&-&-&-&50&270\4&450&-&-&65&-\5&-&255&30&-&-\6&500&-&-&75&- \end{array}$ -What is marginal benefit for the 4^th unit of the activity?

Accepted Answer

The marginal benefit for the 4th unit of the activity is 65. This is because the total benefit increases from 450 to 515 when the level of activity increases from 3 to 4, and the marginal benefit is the change in total benefit divided by the change in level of activity.

Question 5

$\begin{array}{cccccc}
\text { Level of } & \text { Total } & \text { Total } & \text { Marginal } & \text { Marginal } & \text { Net } \
\text { Activit } & \text { Beneft } & \text { Cost } & \text { Benefit } & \text { Cost } & \text { Benefit }\\hline
0&-&0&xx&xx&0\1&200&30&-&-&-\2&-&-&100&-&230\3&-&-&-&50&270\4&450&-&-&65&-\5&-&255&30&-&-\6&500&-&-&75&-
\end{array}$
-The optimal level of activity is:

Accepted Answer

The answer of  
 \(\begin{array}{cccccc}
\text { Level of }...

Question 6

Your firm sells club soda in both grocery stores and convenience stores. You have a budget of $550 for store displays, and must decide how to allocate this budget between grocery stores and convenience stores to maximize the total number of sales. The following table shows the total number of units that can be sold in grocery stores and convenience stores, according to the number of displays in each type of store. Displays in grocery stores cost $150 each and displays in convenience stores cost $100 each.

$\begin{array}{cccc}
&&\text {  number of }\
\text { Number of } & \text { Total number of } & \text { displays in } & \text { Total number of } \
\text { displays in } & \text { units sold in } & \text { convenience } & \text { units sold in } \
\text { grocery stores } & \text { grocery stores } & \text { stores } & \text { convenience stores }\\hline 1 & 500 & l & 400 \
2 & 900 & 2 & 780 \
3 & 1,250 & 3 & 1,130 \
4 & 1,550 & 4 & 1,460 \
5 & 1,750 & 5 & 1,760 \
6 & 1,850 & 6 & 1.960
\end{array}$
-At the optimal choice with a budget of $550, the last dollar spent on grocery store displays yields

Accepted Answer

The optimal allocation of the budget is 2 displays in grocery stores ($300) and 2 displays in convenience stores ($200), totaling $500. The marginal increase in sales from the second to the third display in grocery stores is 350 units (1250 - 900), and the cost is $150, resulting in 350/150 = 2.33 additional sales per dollar. However, the question asks for the last dollar spent, which is the second display, yielding 400/150 = 2.67, rounded to 3.3 additional sales per dollar.

Question 7

$\begin{array}{cccccc}
\text { Level of } & \text { Total } & \text { Total } & \text { Marginal } & \text { Marginal } & \text { Net } \
\text { Activit } & \text { Beneft } & \text { Cost } & \text { Benefit } & \text { Cost } & \text { Benefit }\\hline
0&-&0&xx&xx&0\1&100&50&-&-&-\2&-&-&150&0&100\3&-&-&-&160&115\4&605&-&-&179&-\5&-&674&120&-&-\6&825&-&-&190&-
\end{array}$
-The optimal level of activity is:

Accepted Answer

The answer of  
 \(\begin{array}{cccccc}
\text { Level of }...

Question 8

A computer services center has a problem with "malicious" computer usage. The center's director has decided to hire additional personnel to monitor computer usage. In order to minimize the total cost of the malicious usage, the director should hire the number of monitors at which

Accepted Answer

The director should hire monitors until the decrease in the cost of malicious usage from the last monitor hired equals the cost of hiring the last monitor, which is the point where the marginal benefit equals the marginal cost.

Question 9

$\begin{array}{cccccc}
\text { Level of } & \text { Total } & \text { Total } & \text { Marginal } & \text { Marginal } & \text { Net } \
\text { Activit } & \text { Beneft } & \text { Cost } & \text { Benefit } & \text { Cost } & \text { Benefit }\\hline
0&-&0&xx&xx&0\1&100&50&-&-&-\2&-&-&150&0&100\3&-&-&-&160&115\4&605&-&-&179&-\5&-&674&120&-&-\6&825&-&-&190&-
\end{array}$
-What is marginal benefit for the 3rd unit of the activity?

Accepted Answer

The answer of  
 \(\begin{array}{cccccc}
\text { Level of }...

Question 10

In an unconstrained maximization problem, if at the chosen level of the activity marginal benefit is $60 and marginal cost is $45, a one-unit increase in the activity will _____________________ net benefits by $_________.

Accepted Answer

The answer of In an unconstrained maximization problem, if at...

Question 11

$\begin{array}{cccccc}
\text { Level of } & \text { Total } & \text { Total } & \text { Marginal } & \text { Marginal } & \text { Net } \
\text { Activit } & \text { Beneft } & \text { Cost } & \text { Benefit } & \text { Cost } & \text { Benefit }\\hline
0&-&0&xx&xx&0\1&100&50&-&-&-\2&-&-&150&0&100\3&-&-&-&160&115\4&605&-&-&179&-\5&-&674&120&-&-\6&825&-&-&190&-
\end{array}$
-What is the marginal cost for the 5th unit of the activity?

Accepted Answer

The answer of  
 \(\begin{array}{cccccc}
\text { Level of }...

Question 12

In an unconstrained maximization problem, a reduction in the activity will increase net benefit if _________ ___________ exceeds _________ ___________ .

Accepted Answer

The answer of In an unconstrained maximization problem, a reduction...

Question 13

When making decisions, both _____________ costs and _____________ costs should be ignored, and only _____________ costs and _____________ benefits should be considered.

Accepted Answer

The answer of When making decisions, both _____________ costs and...

Question 14

In an unconstrained maximization problem, if at the chosen level of the activity, marginal benefit is $80 and marginal cost is $90, a one-unit decrease in the activity will _______________ net benefits by $______.

Accepted Answer

The answer of In an unconstrained maximization problem, if at...

Question 15

$\begin{array}{cccccc} \text { Level of } & \text { Total } & \text { Total } & \text { Marginal } & \text { Marginal } & \text { Net } \ \text { Activit } & \text { Beneft } & \text { Cost } & \text { Benefit } & \text { Cost } & \text { Benefit }\\hline 0&-&0&xx&xx&0\1&200&30&-&-&-\2&-&-&100&-&230\3&-&-&-&50&270\4&450&-&-&65&-\5&-&255&30&-&-\6&500&-&-&75&- \end{array}$ -What is the marginal cost of the 1^st unit of the activity?

Accepted Answer

The marginal cost of the 1st unit is the difference in total cost between 1 and 0 units, which is 30 - 0 = 30. None of the given options match this value.

Question 16

Your firm sells club soda in both grocery stores and convenience stores. You have a budget of $550 for store displays, and must decide how to allocate this budget between grocery stores and convenience stores to maximize the total number of sales. The following table shows the total number of units that can be sold in grocery stores and convenience stores, according to the number of displays in each type of store. Displays in grocery stores cost $150 each and displays in convenience stores cost $100 each.

$\begin{array}{cccc}
&&\text {  number of }\
\text { Number of } & \text { Total number of } & \text { displays in } & \text { Total number of } \
\text { displays in } & \text { units sold in } & \text { convenience } & \text { units sold in } \
\text { grocery stores } & \text { grocery stores } & \text { stores } & \text { convenience stores }\\hline 1 & 500 & l & 400 \
2 & 900 & 2 & 780 \
3 & 1,250 & 3 & 1,130 \
4 & 1,550 & 4 & 1,460 \
5 & 1,750 & 5 & 1,760 \
6 & 1,850 & 6 & 1.960
\end{array}$
-To maximize the total number of sales, you should choose

Accepted Answer

The answer of  
Your firm sells club soda in...

Question 17

$\begin{array}{cccccc} \text { Level of } & \text { Total } & \text { Total } & \text { Marginal } & \text { Marginal } & \text { Net } \ \text { Activit } & \text { Beneft } & \text { Cost } & \text { Benefit } & \text { Cost } & \text { Benefit }\\hline 0&-&0&xx&xx&0\1&200&30&-&-&-\2&-&-&100&-&230\3&-&-&-&50&270\4&450&-&-&65&-\5&-&255&30&-&-\6&500&-&-&75&- \end{array}$ -What is the net benefit of the 5^th unit of the activity?

Accepted Answer

The answer of  
 \(\begin{array}{cccccc}
\text { Level of }...

Question 18

A local charity has decided to solicit donations door-to-door. The table below shows estimated donations for each hour a volunteer spends in the city, in the suburbs, and on campus.

$\begin{array}{cccc}
&&\text { Total Donations fiom: }\
\text { Number of Hours } & \text { The city } & \text { The suburbs } & \text { Campus } \
\hline 1 & \$ 75 & \$ 65 & \$ 45 \
2 & 147 & 127 & 87 \
3 & 215 & 185 & 125 \
4 & 279 & 239 & 159 \
5 & 337 & 289 & 189 \
6 & 380 & 333 & 200
\end{array}$
-How should a volunteer allocate 10 hours in order to maximize the amount of total donations?

Accepted Answer

The answer of  
A local charity has decided to...

Question 19

$\begin{array}{cccccc}
\text { Level of } & \text { Total } & \text { Total } & \text { Marginal } & \text { Marginal } & \text { Net } \
\text { Activit } & \text { Beneft } & \text { Cost } & \text { Benefit } & \text { Cost } & \text { Benefit }\\hline
0&-&0&xx&xx&0\1&100&50&-&-&-\2&-&-&150&0&100\3&-&-&-&160&115\4&605&-&-&179&-\5&-&674&120&-&-\6&825&-&-&190&-
\end{array}$
-What is the net benefit of the 6th unit of the activity?

Accepted Answer

The answer of  
 \(\begin{array}{cccccc}
\text { Level of }...

Question 20

A local charity has decided to solicit donations door-to-door. The table below shows estimated donations for each hour a volunteer spends in the city, in the suburbs, and on campus.

$\begin{array}{cccc}
&&\text { Total Donations fiom: }\
\text { Number of Hours } & \text { The city } & \text { The suburbs } & \text { Campus } \
\hline 1 & \$ 75 & \$ 65 & \$ 45 \
2 & 147 & 127 & 87 \
3 & 215 & 185 & 125 \
4 & 279 & 239 & 159 \
5 & 337 & 289 & 189 \
6 & 380 & 333 & 200
\end{array}$
-Given an optimizing solution, the fourth hour solicited yielded

Accepted Answer

The additional donations for the fourth hour are calculated by subtracting the total donations for three hours from the total donations for four hours in the city: $279 - $215 = $64.

Quiz 3: Marginal Analysis for Optimal Decisions

A package delivery service currently has 12 vans and 16 employees. Vans cost $400 per week and employees earn $300 per week. The last van added 480 packages delivered to total output, while the last employee added 450 packages. The firm

A computer services center has a problem with "malicious" computer usage. The center's director has decided to hire additional personnel to monitor computer usage. In order to minimize the total cost of the malicious usage, the director should hire the number of monitors at which

In an unconstrained maximization problem, if at the chosen level of the activity marginal benefit is $60 and marginal cost is $45, a one-unit increase in the activity will _____________ net benefits by $_.

In an unconstrained maximization problem, a reduction in the activity will increase net benefit if ___ _ exceeds _ _______ .

When making decisions, both _______ costs and _ costs should be ignored, and only _ costs and _______ benefits should be considered.

In an unconstrained maximization problem, if at the chosen level of the activity, marginal benefit is $80 and marginal cost is $90, a one-unit decrease in the activity will _________ net benefits by $.