Question

In: Finance

Justin Brody is the production manager for a math textbook manufacturing company. The company produces Geometry...

Justin Brody is the production manager for a math textbook manufacturing company. The company produces Geometry and Calculus texts. Each Geometry text generates a profit of $80 and requires 3 hours assembly time and 4 hours of proofing. Each Calculus text generates $45 of profit and requires 5 hours of assembly and 2 hours of proofing. There are 360 hours of assembly time and 240 hours of proofing time available each month.

Find the number of Geometry and Calculus texts to make that maximizes the profit each month.

Solutions

Expert Solution

Assume , Number of Geometry Text=X

Number of Calculus Text=Y

Maximize Profit =Z=80X+45Y

Constraints:

3X+5Y< or=360

4X+2Y< or=240

The point of maximum profit will be at the intersection of the following equations:

3X+5Y=360................(1)

4X+2Y=240...............(2)

Multiply equation (1) by 4

12X+20Y=1440......(3)

Multiply equation (2) by 3

12X+6Y=720.........(4)

Subtracting (4) from (3)

14Y=720

Y=720/14=51.4

Substituting Y in Equation(1)

3X+5*51.4=360

3X=360-5*51.4=103

X=103/3=34.3

Ronuded to nearest whole number:

Number of Geometry Text=X=34

Number of Calculus Text=Y=51

PROFIT=Z=80*34+45*51=5015

Constraints:

3*34+5*51=357< 360

4*34+2*51=238< 240

Number of Geometry Text=X=34

Number of Calculus Text=Y=51


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