Question

Punk and Pawn manufactures hockey sticks and chess sets. Each hockey stick yields a profit of $2, and each chess set yields $4 profit.A hockey stick requires 4 hours of processing at Machine Center A and 2 hours at Machine Center B.Each chess set requires 6 hours at machine center A and 6 hour at machine center B, and 1 hour at Machine Center C.Machine center A has a maximum of 120 hours of available capacity per day;Machine Center B has 72 hour capacity per day; and Machine Center C has 10 hours capacity per day.The manufacturer seeks to maximize daily profits.Clearly state yourdecision variables and formulate a linear program that maximizes profit for the company

Answer 1

Let H be denoted as number of hockey stcicks and C be denoted as number of Chess sets

Here objective is to maximize profit.

The profit for each hockey stick is $2, and

The profit for each Chess set is $4

Therefore the Objective function is

Maximize Z = 2H+4C

Now the constraints will be

For Machine Center A , we have maximum 120 hours, and the processing time for each hockey is 4 hrs and the processing time for each chess set is 6 hrs.

Therefore , the constraint for Machine Center A

For Machine Center B, the maximum capacity is 72 hours per day. And the processing time for each hockey is 2hrs and the processing time for each chess set is 6 hrs.

Therefore , the constraint for Machine Center B is

For Machine C, the maximum capacity per day is 10 hours, and only chess sets requires processing time on Machine C of 1hour.

Therefore , the constraint for Machine Center 1C

Since the number of hockey sticks and chess set cannot be less than zero, we have the constraint

therefore the LPP is

Obj. function Maximize Z = 2H+4C

Subject to