Question

Outdoor Joy is a company that sells outdoor patio equipment and grills. They are planning for a big Summer sale and are wondering how they should spend their marketing dollars. They have used 4 different marketing media in the past and recognize that each media reaches a different customer base. Because of this, management has established minimum and maximums for each type of media. Using historic data, they have estimated the revenue that a unit of each media would generate.

Media	Cost per Unit	Revenue	Minimum Units	Maximum Units
Television	$5,000	$37,500	3	6
Radio	$750	$12,800	2	10
Direct Mail	$2,000	$13,000	2	10
Online	$1,000	$42,000	3	8

Outdoor Joy can only purchase whole units of a media and have a budget of $35,000 to spend. Maximize their expected revenue using optimization.

1. Should integer optimization be used in this case? Answer with Yes or No.

2. What is their maximum revenue? (Do not include $ and commas in your answer.)

3. How many units of Television should they purchase?

Please show work in excel.

Answer 1

1. Yes, integer optimization should be used in this case, since fractional values of any of these media cannot be bought

2. The maximum value is 602500

3. They should purchase 3 units of television

Pls refer to the table below.

Media	Cost per Unit	Revenue	Minimum Units	Maximum Units	Units
Television	$5,000	$37,500	3	6	A
Radio	$750	$12,800	2	10	B
Direct Mail	$2,000	$13,000	2	10	C
Online	$1,000	$42,000	3	8	D
Budget	35000
Maximize	37500A + 12800B + 13000C + 42000D
Subject to the following
	5000A+750B+2000C+1000D <=35000
	A is between 3 and 6
	B is between 2 and 10
	C is between 2 and 10
	D is between 3 and 8
	A, B, C and D are integers
We use solver in this system
	A	B	C	D
Units (to solve for)	3	10	2	8
Profit	37500	12800	13000	42000	602500	maximize
Budget	5000	750	2000	1000	34500	35000	less than or equal to
A					3	3	greater than or equal to
A					3	6	less than or equal to
B					10	2	greater than or equal to
B					10	10	less than or equal to
C					2	2	greater than or equal to
C					2	10	less than or equal to
D					8	3	greater than or equal to
D					8	8	less than or equal to