Question

Problem #32) Diamond Jewelers is trying to determine how to advertise in order to maximize their exposure. Their weekly advertising budget is $10,000. They are considering three possible media: TV, newspaper, and radio. Information regarding cost and exposure is given in the table below:

Medium	audience reached per ad	cost per ad ($)	maximum ads per week
TV (T)	7,000	800	10
Newspaper (N)	8,500	1000	7
Radio (R)	3,000	400	20

Based on problem #32, which of the following sets of constraints properly represent the limits on advertisements per week by media?

A) T ≤ 10; N ≤ 7; R ≤ 20

B) T ≥ 10; N ≥ 7; R ≥ 20

C) T + R + N ≤ 37

D) T + R + N ≥ 37

Based on problem #32, what is the optimal solution?

A) T = 10; N = 7; R = 20

B) T = 10; N = 0; R = 0

C) T = 10; N = 2; R = 0

D) T = 10; N = 20; R = 7

Answer 1

Answer 1)

Since maximum ads for T,N and R should be less than 10,7 and 20, individually, the Option A is appropriate.

The Option B limits imply that the minimum ads for T,N and R should be 10,7 and 20, which is exactly the opposite of the requirement.

Options C & D consider the limitation of ads on a total basis, which has not been required by the question. The question places limits on each ad type, not in totality.

Answer 2)

There are 2 constraints in this question:

1. T ≤ 10; N ≤ 7; R ≤ 20
2. Weekly ad spend <=10,000

Using Simplex function on Excel, the appropriate answer is Option C i.e. T = 10; N = 2; R = 0.

Following is the working:

Note: Please levae cells C10 - C12 blank so as to arrive at the answer using Solver.

Calculations are given as under:

The parameters are given as under:

If the use of Excel is not permitted, you may evalauate each of the options subject to the constraints mentioned above, in which case:

• Options A & D result in the ad budget going beyond $10,000
• Option B does not give the maximum profit possible.

Thus, by virtue of elimination, Option C seems the most appropriate.

In case of any questions on the above workings, please share the same in the comments section.

All the best!