Answer to Question #289823 in Operations Research for Panya

Question #289823

ABC company manufactures and sells two products P1 and P2. Each unit of P1 requires two hours of machining and one hour of skilled labour. Each unit of P2 requires one hour of machining and two hours of labour. The machine capacity is limited to 650 man hours. Only 300 unit's of product P1 can be sold in the market. The per unit contribution from product P1 is Ksh. 80 and product P2 is Ksh. 120 . Formulate a linear programming model


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Expert's answer
2022-01-25T14:14:24-0500

Let the number of products P1P_1 and P2P_2 produced be x1x_1 and x2x_2 respectively.

The objective function zz which is the contribution from each product and which is to be maximized is given as:


z=80x1+120x2z=80x_1+120x_2

We have two constraints, which are; time on machining and skilled labour.

For machining, the limit is 600 hours. So, we have:


2x1+x26002x_1+x_2\leq 600

For skilled labour, the limit is 650 hours. So, we have:


x1+2x2650x_1+2x_2 \leq 650

There is a constraint on the number of product P1P_1 that can be sold. So, we have:


x1300x_1 \leq 300

Bringing everything together, we have:


Maximize:                      z=80x1+120x2Subject to :                                                                                     2x1+x2600                                  x1+2x2650                                  x1          300 x1,x20\text{Maximize:}~~~~~~~~~~~~~~~~~~~~~~z=80x_1+120x_2\\ \text{Subject to~: }~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\\ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~2x_1+x_2\leq 600\\ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~x_1+2x_2 \leq 650\\ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~x_1~~~~~~~~~~\leq 300~\\ x_1,x_2 \geq0



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