Question

Let us move to linear programming

1. FIRMCo is planning an advertising campaign, budgeted at $70000. Each 1000 dollars spent on radio ads, results in 70 new customers. Similarly, each 1000 dollars spent on TV ads yield 105 new customers. Each radio ad costs $250, and each TV ad costs $1500. The combined number of ads used in the campaign cannot exceed 75. The amount spent on radio ads, and the amount spent on TV ads cannot differ from one another by more than $15000. Define the two decision variables by R and TV (the amount in thousand dollars, spent on radio ads and TV ads. For example, if R=7 then 7000 is spent on radio ads. Answer the following questions about the linear programming model that maximizes the number of new customers.

2.1 The objective function is:

1. Max (1000*R)/70 + (1000*TV)/105
2. Max 70R + 105*TV
3. Max (70+105)*1000*(R+TV)

2.2 The budget constraint is:

a. R + TV <= 70000

b. R/1000 + TV/1000 <= 70

c. R + TV <= 70
2.3 The constraint on the combined number of ads is:
       a. (R*250 + TV*1500)/70 >= 75

       b. 1000R/250 + 1000TV/1500 <= 75
       c. R/250 + TV/1500 <=70000/75

       d. (R+TV)/(250+1500) <=75

2.4 The constraint (or constraints) on the amounts spent on the two media is:

       a. We need two constraints: R – TV <= 15, and TV – R <= 15.

       b. We can either use R – TV <= 15, or TV – R <= 15, but not both.

       c. We need two constraints: R <= 15 and TV >= 15.

d. R – TV >= 15, and TV – R >= 15

Answer 1

Ans :- We define R as the amount in thousand dollars on radio ads

and TV as the amount in thousand dollars on TV ads

2.1 The objective function is to maximise the number of new customers

Max 70*R + 105*TV

2.2 the budget constraitn is that it cannot exceed 70000

R + TV <= 70 (since R and TV already measured in thousand of dollars)

2.3 The constraint on the combined number of ads is: they should not exceed 75 combinedly

1000R/250 + 1000TV/1500 <= 75

2.4 The constraint (or constraints) on the amounts spent on the two media is:The amount spent on radio ads, and the amount spent on TV ads cannot differ from one another by more than $15000.

We need two constraints: R – TV <= 15, and TV – R <= 15.