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.

1 Farmer Jones must determine how many acres of corn and wheat to plant this year. An acre of wheat yields 25 bushels of wheat and requires 10 hours of labor per week. An acre of corn yields 10 bushels of corn and requires 4 hours of labor per week. All wheat can be sold at $S4 a bushel, and all corn can be sold at S3 a bushel. Seven acres of land and 40 hours per week of labor are available Government regulations require that at least 30 bushels of corn be produced during the current year. Let x1 - number of acres of corn planted, and x2-number of acres of wheat planted. Using these decision variables, formulate an LP whose solution will tell Farmer Jones how to maximize the total revenue from wheat and corn.

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