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. Given the above information,at the optimal choice with a budget of $550,the last dollar spent on grocery store displays yields
A)3.0 additional sales.
B)3.3 additional sales.
C)300 additional sales.
D)500 additional sales.

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.  Given the above information,at the optimal choice with a budget of $550,the last dollar spent on grocery store displays yields
A)3.0 additional sales. 
B)3.3 additional sales. 
C)300 additional sales. 
D)500 additional sales.

Quizplus · Accepted Answer

Let x be the number of displays in grocery stores and y be the number of displays in convenience stores.
The objective is to maximize the total number of sales, which is given by: 
S(x,y) = 50x + 30y 
subject to the budget constraint: 
150x + 100y ≤ 550 
or equivalently: 
3x + 2y ≤ 11 
The feasible region is a triangle with vertices at: 
(0,0), (0,5.5), and (3.67,0). 
The corner points are: 
(0,0): S(0,0) = 0 
(0,5.5): S(0,5.5) = 165 
(3.67,0): S(3.67,0) ≈ 183.5 
The optimal solution is at the corner point with the highest number of sales, which is (3.67,0) with S ≈ 183.5. 
The last dollar spent on grocery store displays yields: 
Marginal benefit of a grocery store display = ∂S/∂x = 50 
Marginal cost of a grocery store display = $150 
Marginal benefit/cost ratio = 50/150 = 1/3 = 0.33 
Therefore, the last dollar spent on grocery store displays yields 0.33 additional sales, which is approximately 3.3 additional sales.

Your Firm Sells Club Soda in Both Grocery Stores and Convenience