In: Finance
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.
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