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

Question

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

Quizplus · 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.

Your Firm Sells Club Soda in Both Grocery Stores and Convenience