Peters Company, Inc., is a manufacturer of widgets. It manufactures two types of

Question

Peters Company, Inc., is a manufacturer of widgets. It manufactures two types of widgets Widgets A and Widgets B. The Profit contribution of each type of widget is P 6.00 & P 5.00, respectively. Mr. Peters, the owner of Company, Inc., found out that his weekly available supply of raw material 1 (RM1) and raw material 2 (RM2) are 30 units and 30 units, respectively. Each unit of Widget A requires 5 units of RM1 and 4 units of RM2 while each unit of Widget B requires 4 units of RM1 and 5 units of RM2. Weekly demand for Widget A is 5 units while that for Widget B is 8 units. Weekly plant capacity of Widget, Inc. is 7 units for Widget A and 5 units for Widget B. Formulate an LP Model for the Peters Company, Inc. that will optimize its profit. X1 RHS Max. or Min Raw Mat. 1 Raw Mat. 2 Demand A Demand B Capacity A Capacity B

Explanation / Answer

Formulation

Max. Z = 6X1 + 5X2
Subject to,
5X1 + 4X2 <= 30 (RM 1)
4X1 + 5X2 <= 30 (RM 2)
1X1 + 0X2 <= 5 (Demand of A)
0X1 + 1X2 <= 8 (Demand of B)
1X1 + 0X2 <= 7 (Capacity of A)
0X1 + 1X2 <= 5 (Capacity of B)
X1, X2 >= 0

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Qty. of widget A Qty. of widget B X1 X2 RHS Max. 6 5 Raw mat. 1 5 4 <= 30 Raw mat. 2 4 5 <= 30 Demand A 1 0 <= 5 Demand B 0 1 <= 8 Capacity A 1 0 <= 7 Capacity B 0 1 <= 5

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