Question 1

Determine the values of x and y that produce the maximum value of the objective function on the feasible
region. Determine the maximum value of the objective function on the feasible region.
-$$\begin{array} { l } 
x \geq 0 , y \geq 0 \
110 x + 70 y \leq 8,600 \
x + y \leq 100 \
\quad \text { Maximize: } z = 35 x + 30 y
\end{array}$$
A) $x = 55 , y = 45$; Maximum value: 3,275
B) $x = 40 , y = 60$; Maximum value: 3,200
C) $x = 45 , y = 55$; Maximum value: 3,225
D) $x = 60 , y = 40$; Maximum value: 3,300

Accepted Answer

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Question 2

Determine the values of x and y that produce the minimum value of the objective function on the given
feasible region.
-Minimize: $z = 4 x + 3 y$

A) $x = 6 , y = 2$
B) $x = 2 , y = 8$
C) $x = 7 , y = 10$
D) $x = 8 , y = 4$

Accepted Answer

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Question 3

Choose the one alternative that best completes the statement or answers the question.
Solve the problem.
-The cost for an animal shelter to spay a female cat is $87 and the cost to neuter a male cat is $59. Write an objective function z = f (x, y) that represents the total cost for spaying x female cats and Neutering y male cats. 
A) $z = 87 x + 59 y$
B) $z = 73 ( x + y )$
C) $z = 59 x + 87 y$
D) $z = 28 ( x + y )$

Accepted Answer

The objective function $z = 87x + 59y$ correctly represents the total cost, with $87 being the cost to spay each female cat (x) and $59 being the cost to neuter each male cat (y).

Question 4

Determine the maximum value of the objective function on the given feasible region.
-Maximize: $z = 4 x + 3 y$

A) Maximum value: 26
B) Maximum value: 32
C) Maximum value: 33
D) Maximum value: 38

Accepted Answer

The answer of Determine the maximum value of the objective...

Question 5

Determine the values of x and y that produce the maximum value of the objective function on the given
feasible region.
-$\text { Maximize: } z = 300 x + 150 y$

A) $x = 20 , y = 20$
B) $x = 20 , y = 40$
C) $x = 0 , y = 0$
D) $x = 60 , y = 0$

Accepted Answer

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Question 6

Solve the problem.
-A plant nursery sells two sizes of oak trees to landscapers. Large trees cost the nursery $120 from the grower and small trees cost $70. The profit for each large tree sold is $40, and the profit for each
Small tree sold is $25. The monthly demand is at most 475 oak trees. Furthermore, the nursery does
Not want to allocate more than $43,000 each month on inventory for oak trees. Determine the
Number of large oak trees and the number of small oak trees that the nursery should have in its
Inventory each month to maximize profit, and determine the maximum profit. (Assume that all trees
In inventory are sold.)
A) 275 large oaks and 200 small oaks for a maximum profit of $16,000.
B) 280 large oaks and 195 small oaks for a maximum profit of $16,075.
C) 200 large oaks and 275 small oaks for a maximum profit of $14,875.
D) 195 large oaks and 280 small oaks for a maximum profit of $14,800.

Accepted Answer

The answer of Solve the problem.
-A plant nursery sells two...

Question 7

Write the word or phrase that best completes each statement or answers the question.
Provide the missing information.
-The points of intersection of a feasible region are called the ________of the region.

Accepted Answer

The answer of Write the word or phrase that best...

Question 8

Choose the one alternative that best completes the statement or answers the question.
Solve the problem.
-A diner makes a profit of $1.30 for a cup of coffee and $1.10 for a cup of tea. Write an objective function z = f(x, y) that represents the total profit for selling x cups of coffee and y cups of tea. 
A) $z = 0.20 ( x + y )$
B) $z = 1.30 x + 1.10 y$
C) $z = 1.10 x + 1.30 y$
D) $z = 2.40 ( x + y )$

Accepted Answer

The objective function that represents the total profit for selling x cups of coffee and y cups of tea, with a profit of $1.30 per cup of coffee and $1.10 per cup of tea, is $z = 1.30x + 1.10y$.

Question 9

Solve the problem.
-A large department store needs at least 3,200 labor hours covered per week. It employs full-time staff 40 hr/wk and part-time staff 30 hr/wk. The cost to employ a full-time staff member is more
Because the company pays benefits such as health care and life insurance. $$\begin{array} { l | c | c } 
& \text { Hours per Week } & \text { Cost per Hour } \
\hline \text { Full-time } & 40 & 20 \
\text { Part-time } & 30 & 13
\end{array}$$ The store manager also knows that to make the store run efficiently, the number of full-time employees must
Be at least 1.25 times the number of part-time employees. Determine the number of full-time
Employees and the number of part-time employees that should be used to minimize the weekly labor
Cost. What is the minimum weekly cost to staff the store under these conditions.
A) 40 full-time employees and 50 part-time employees for a minimum cost of $1,450.
B) 50 full-time employees and 40 part-time employees for a minimum cost of $1,520.
C) 40 full-time employees and 50 part-time employees for a minimum cost of $51,500.
D) 50 full-time employees and 40 part-time employees for a minimum cost of $55,600.

Accepted Answer

To solve this, we set up equations based on the given information. Let $F$ be the number of full-time employees and $P$ be the number of part-time employees. The total hours equation is $40F + 30P \geq 3200$, and the condition for full-time employees is $F \geq 1.25P$. The cost function to minimize is $20(40F) + 13(30P)$. Solving these equations with the constraints, we find that 50 full-time employees and 40 part-time employees minimize the cost, which calculates to $55,600.

Question 10

Determine the values of x and y that produce the minimum value of the objective function on the feasible
region. Determine the minimum value of the objective function on the feasible region.
-$$\begin{array} { l } 
x \geq 0 , y \geq 0 \
40 x + 30 y \geq 3,200 \
x \geq 1.75 y \
\quad \text { Minimize } z = 22 x + 12 y
\end{array}$$
A) $x = 32 , y = 56$; Minimum value: 48,320
B) $x = 32 , y = 56$; Minimum value: 1,376
C) $x = 56 , y = 32$; Minimum value: 60,800
D) $x = 56 , y = 32$; Minimum value: 1,616

Accepted Answer

To find the minimum value of the objective function $z = 22x + 12y$ given the constraints, we first identify the feasible region defined by the constraints $x \geq 0$, $y \geq 0$, $40x + 30y \geq 3200$, and $x \geq 1.75y$. The minimum value of $z$ occurs at a vertex of the feasible region. By substituting the equality conditions of the constraints into the objective function, we can find the values of $x$ and $y$ that minimize $z$. Given the constraints, the point $x = 56, y = 32$ is on the boundary of the feasible region and satisfies all constraints. Substituting these values into the objective function gives $z = 22(56) + 12(32) = 1232 + 384 = 1616$, which is the minimum value of the objective function.

Question 11

Solve the problem.
-A furniture manufacturer builds tables. The cost for materials and labor to build a kitchen table is $270 and the profit is $180. The cost to build a dining room table is $300 and the profit is $220. Let
X represent the number of kitchen tables produced per month. Let y represent the number of dining room
Tables produced per month.
The manufacturing process is subject to the following constraints.
1) The number of each type of table cannot be negative.
2) Due to labor and equipment restrictions, the company can build at most 110 kitchen tables.
3) The company can build at most 70 dining room tables.
4) The company does not want to exceed a monthly cost of $48,000. a. Write an objective function representing the monthly profit for producing and selling $x$ kitcher tables and y dining room tables.
b. How many kitchen tables and how many dining room tables should be produced to maximize profit? (Assume that all tables produced will be sold.)
A) $z = 180 x + 220 y ; 100$ kitchen tables and 70 dining room tables
B) $z = 220 x + 180 y ; 61$ kitchen tables and 110 dining room tables
C) $z = 180 x + 220 y ; 110$ kitchen tables and 61 dining room tables
D) $z = 220 x + 180 y ; 70$ kitchen tables and 100 dining room tables

Accepted Answer

The objective function for profit is $z = 180x + 220y$ because the profit from each kitchen table is $180 and from each dining room table is $220. To maximize profit without exceeding the monthly cost limit, producing 100 kitchen tables and 70 dining room tables utilizes the budget and production capacity efficiently.

Question 12

Determine the values of x and y that produce the minimum value of the objective function on the given
feasible region.
-Minimize $z = 7 x + 3 y$

A) $x = 0 , y = 0$
B) $x = 25 , y = 0$
C) $x = 15 , y = 20$
D) $x = 0 , y = 65$

Accepted Answer

The answer of Determine the values of x and y...

Question 13

Solve the problem.
-A manufacturer produces two models of a gas grill.Grill A requires 0.9 hr for assembly and 0.5 hr for packaging. Grill B requires 1.2 hr for assembly and 0.8 hr for packaging. The production Information and profit for each grill are given in the table. The manufacturer has 1,152 hr of labor Available for assembly and 716 hr of labor available for packaging. $\begin{array} { l | c | c | c } 
& \text { Assembly } & \text { Packaging } & \text { Profit } \
\hline \text { Grill A } & 0.9 \mathrm { hr } & 0.5 \mathrm { hr } & 80 \
\text { Grill B } & 1.2 \mathrm { hr } & 0.8 \mathrm { hr } & 110
\end{array}$
a. Determine the number of grill A units and the number of grill B units that should be produced to Maximize profit assuming that all grills will be sold.
b. What is the maximum profit under these constraints?
c. If the profit on grill A units is 120 and the profit on grill B units is unchanged, how many of each Type of grill unit should the manufacturer produce to maximize profit?

A) a. $\mathrm { A } = 0 , \mathrm {~B} = 895$
b. Profit $= 98,450$
c. 520 units of $A$ and 570 units of B

B) a. $A = 520 , B = 570$
b. Profit = 57,656
c. 1,280 units of A and 0 units of B

C) a. $\mathrm { A } = 520 , \mathrm {~B} = 570$
b. Profit $= 104,300$
c. 1,280 units of $\mathrm { A }$ and 0 units of $\mathrm { B }$

D) $\mathbf { a } . \mathrm { A } = 1,280 , \mathrm {~B} = 0$
b. Profit $= 102,400$
c. 1,280 units of $\mathrm { A }$ and 0 units of $\mathrm { B }$

Accepted Answer

To solve this linear programming problem, we set up equations based on the given constraints and aim to maximize profit. For part a, using the constraints of assembly and packaging hours, we find the combination of Grill A and Grill B units that maximizes profit without exceeding the available hours. For part b, we calculate the total profit based on the optimal number of units found in part a. For part c, after changing the profit of Grill A, we recalculate to find the new optimal production plan that maximizes profit. The correct answer reflects the combination of Grill A and Grill B units that maximizes profit under the given constraints, the maximum profit achievable, and the adjusted production plan after changing the profit of Grill A.

Question 14

Determine the values of x and y that produce the maximum value of the objective function on the given feasible region.
-$\text { Maximize: } z = 2 x + 3 y$

A) $x = 0 , y = 9$
B) $x = 9 , y = 0$
C) $x = 6 , y = 2$
D) $x = 4 , y = 7$

Accepted Answer

The answer of Determine the values of x and y...

Question 15

Determine the values of x and y that produce the maximum value of the objective function on the given feasible region.
-Maximize $z = 40 x + 50 y$

A) $x = 10 , y = 4$
B) $x = 0 , y = 8$
C) $x = 10 , y = 0$
D) $x = 6 , y = 8$

Accepted Answer

The answer of Determine the values of x and y...

Quiz 5: Systems of Equations and Inequalities

Determine the values of x and y that produce the minimum value of the objective function on the given feasible region. -Minimize: z=4x+3yz = 4 x + 3 yz=4x+3y

Determine the maximum value of the objective function on the given feasible region. -Maximize: z=4x+3yz = 4 x + 3 yz=4x+3y

Determine the values of x and y that produce the maximum value of the objective function on the given feasible region. - Maximize: z=300x+150y\text { Maximize: } z = 300 x + 150 y Maximize: z=300x+150y

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -The points of intersection of a feasible region are called the ________of the region.

Determine the values of x and y that produce the minimum value of the objective function on the given feasible region. -Minimize z=7x+3yz = 7 x + 3 yz=7x+3y

Determine the values of x and y that produce the maximum value of the objective function on the given feasible region. - Maximize: z=2x+3y\text { Maximize: } z = 2 x + 3 y Maximize: z=2x+3y

Determine the values of x and y that produce the maximum value of the objective function on the given feasible region. -Maximize z=40x+50yz = 40 x + 50 yz=40x+50y

Determine the values of x and y that produce the minimum value of the objective function on the given feasible region. -Minimize: $z = 4 x + 3 y$

Determine the maximum value of the objective function on the given feasible region. -Maximize: $z = 4 x + 3 y$

Determine the values of x and y that produce the minimum value of the objective function on the given feasible region. -Minimize $z = 7 x + 3 y$

Determine the values of x and y that produce the maximum value of the objective function on the given feasible region. -Maximize $z = 40 x + 50 y$