Question

BP Cola Must Decide How Much Money To Allocate For New Soda And Traditional Soda Advertising ... Question: BP Cola must decide how much money to allocate for new soda and traditional soda advertising over... BP Cola must decide how much money to allocate for new soda and traditional soda advertising over the coming year. The advertising budget is $10,000,000. Because BP wants to push its new sodas, at least one-half of the advertising budget is to be devoted to new soda advertising. However, at least $2,000,000 is to be spent on its traditional sodas. BP estimates that each dollar spent on traditional sodas will translate into 100 cans sold, whereas, because of the harder sell needed for new products, each dollar spent on new sodas will translate into 50 cans sold. To attract new customers BP has lowered its profit margin on new sodas to 2 cents per can as compared to 4 cents per can for traditional sodas. How should BP allocate its advertising budget if it wants to maximize its profits while selling at least 750 million cans?

Answer 1

The question is about allocation of fundstowards promotion of new sodas and traditional sadas with the objective to maximize profits while selling at least 780 million cans.

Profit margin on new sodas is 2 cents per can and 4 cents per can for traditional sodas.

Let X be the amount for new sodas and Y be the amount for old ones. Therefore, X + Y = 10,000,000 and as per the conditions stated, X >= 5,000,000 and Y >= 2,000,000

Constraint in terms of number of cans is 50X + 100Y >= 750,000,000

Objective function is to Maximize 100X + 400Y

Solution to the above linear programming problem is as follows:

As number of cans as well as profit per can is more in the case of traditional sodas, therefore only $5,000,000 (at least) are allocated to promotion of new sodas with sales of 250,000,000 cans and remaining $5,000,000 for traditional sodas for sales of 500,000,000 cans.

Details of formulation and solution as follows:

	X	Y		RHS	Equation form
Maximize	100	400			Max 100X + 400Y
Total	1	1	<=	1,00,00,000	X + Y <= 1E+07
new	1	0	>=	50,00,000	X >= 5000000
old	0	1	>=	20,00,000	Y >= 2000000
numberCan	50	100	>=	75,00,00,000	50X + 100Y >= 7.5E+08

Variable	Status	Value
X	Basic	50,00,000
Y	Basic	50,00,000
slack 1	NONBasic	0
surplus 2	NONBasic	0
surplus 3	Basic	30,00,000
surplus 4	Basic	0
Optimal Value (Z)		2,50,00,00,000