This is a question for the book Operations Research by Winst

This is a question for the book (Operations Research by Winston) and for the topic of (introduction to linear programming) for an industrial engineering class.

8 Highland\'s TV-Radio Store must determine how many TVs and radios to keep in stock. A TV requires 10 sq ft of floorspace, whereas a radio requires 4 sq ft; 200 sq ft of floorspace is available. A TV will earn Highland $60 in profits, and a radio will earn $20. The store stocks only TVs and radios. Marketing requirements dictate that at least 60% of all appliances in stock be radios. Finally, a TV ties up $200 in capital, and a radio, S50. Highland wants to have at most $3,000 worth of capital tied up at any time. Formulate an LP that can be used to maximize Highland\'s profit.

Solution

Decision variable = x1,x2

Constraints:

7 acres of land are available: x1+x2<=7

40 hours of labour are available: 4x1+10x2<=40

Atleast 30 bushel of corn has to be produced: x1>=30

Revenue= 10*3*x1+25*4*x2=30x1+100x2

Final LP Model:

Maximize: 30x1+100x2

Subject to:

x1+x2<=7

4x1+10x2<=40

x1>=30

x2>=0

The solution of the above LP will tell farmer jones how to maximize the total revenue from wheat and corn