Question

A manufacturer makes two types of handmade fancy paper bags: type A and type B. Two designers—a cutter and a finisher—need to work on both kinds of bags. A type A bag requires 2 hours of the cutter's time and 1 hour of the finisher's time. A type B bag requires 1 hour of the cutter's time and 2 hours of the finisher's time. Each month the cutter is available for 104 hours and the finisher is available for 76 hours. The manufacturer gets a profit of $6 on each bag of type A and $11 on each bag of type B. Identify the number of bags of each type to be manufactured to obtain maximum profit.

Answer 1

Answer:

Type A to produce 44 bags and Type B to produce 16 bags to maximize profit of $440

Explanation:

Let X be the number of bags for Type A and Y be the number of bags for Type  B

                                      Cutter              Finisher

Type A                              2X                   1X    =   $6X

Type B                               1Y                   2Y     =  $11Y

                                        104                  76

2x+1y= 104

1x+2y=76

y= 104-2x

x+2(104-2x) = 76

x+ 208-4x = 76

132= 3x

x= 44 bags

y= 104-2(44)

y= 16 bags

Type A should produce 44 bags and Type B 16 bags to maximize profit

Maximum Profit = 6X + 11Y

                         = 6(44) + 11(16)

                        = $440