Question

The marketing manager for Mountain Mist soda needs to decide how many TV spots and magazine ads to run during the next quarter. • Each TV spot costs $7000 and is expected to increase sales by 420,000 cases. • Each magazine ad costs $2500 and is expected to increase sales by 500,000 cases. • A total of $100,000 may be spent on TV and magazine ads combined. However Mountain mist wants to spend no more than $70,000 on TV spots and no more than $50,000 on magazine ads. Mountain Mist earns a profit margin of $1.80 on each case of soda that it sells, not factoring in marketing costs (just operational profit). Formulate this problem as a linear program to MAXIMIZE NET INCOME (operational profit less advertising costs), where Decision Variables are A=Number of TV spots, B=Number of Magazine Ads. Do not use Excel for this, just algebra.

Answer 1

Answer: The LP model is given as :

max: 1.180( 420000 A + 500000 B )

subject to : (a.) 7000 A + 2500 B ≤ 100000

(b.) 7000 A ≤ 70000

(c.) 2500 B ≤ 50000

Explanation:

Let us assume;

A be the no. of T.V spots

B be the no. of magazine spots

Given:

(a.) Mountain Mist earns a profit margin of $1.80 on each case of soda that it sells.

(b.) Each TV spot costs $7000 and is expected to increase sales by 420,000 cases.

(c.) Each magazine ad costs $2500 and is expected to increase sales by 500,000 cases.

∴ The objective function of this model will be given as :

max: 1.180( 420000 A + 500000 B )

(d.) A total of $100,000 may be spent on TV and magazine ads combined.

(e.) Mountain mist wants to spend no more than $70,000 on TV spots and no more than $50,000 on magazine ads.

∴ The subjective function will be :

(a.) 7000 A + 2500 B ≤ 100000

(b.) 7000 A ≤ 70000

(c.) 2500 B ≤ 50000

∴ The LP model is given as :

max: 1.180( 420000 A + 500000 B )

subject to : (a.) 7000 A + 2500 B ≤ 100000

(b.) 7000 A ≤ 70000

(c.) 2500 B ≤ 50000