Question

SOLVER EXCEL Turley Tailor Inc. makes shirts, Jackets, and coats. A shirt requires 1 hour of cutting and 5 hours of sewing. A jacket requires 2 hour of cutting and 4 hours of sewing. A coat requires 4 hours of cutting and 3 hours of sewing. There are a maximum of 138 hours of labor in the cutting department each day and 105 hours in the sewing department. The maximum number of coats that can be produced is two more than the number of shirts Hourly labor rate for sewing is $2.5 and for cutting is $3.4. Each shirt price is $126 each jacket is $177, and each coat $257. Find the number of shirts, jacket, and coats to produce the maximum profit. What is this maximum profit?

Answer 1

Say, maximum number of shirt and jacket is x and y respectively. Number of coats is (x+2)

Total Revenue= x*126+y*177+257*(x+2)=383x+177y+514

Total Labor cost for sewing= (x*5+y*4+(x+2)*3)*2.5=12.5x+10y+7.5x+15=20x+10y+15

Total labor cost for cutting= (x*1+y*2+(x+2)*4)*3.4=3.4x+6.8y+13.6x+27.2=17x+6.8y+27.2

Maximum Labor hour for cutting=x*1+y*2+(x+2)*4=x+2y+4x+8=5x+2y+8=138

or, 5x+2y=130

Similarly, Labor hour for sewing= x*5+y*4+(x+2)*3=105

or, 5x+4y+3x+6=105

or, 8x+4y=99

Solving, the above 2 equation, x= 85.5 and y=-146.25

So, as jacket can't be produced at maximum capacity,maximum profit can't be acheived.