A company manufactures products A, B, C, D, & E. Contribution margin per unit fo

Question

A company manufactures products A, B, C, D, & E. Contribution margin per unit for each product are 12, 18, 9, 11, and 4, respectively. Consumption rates of these Products for Raw Material 1 are 2, 3, 2, 2, and 1 while those for Raw Material 2 are 3, 5, 4, 3, and 3, also respectively. There are 1,000 units of Raw Material 1 and 2,000 units of Raw Material 2. Volume demands for products A, B, C, and D are 400, 500, 300, and 280 units while committed delivery for Product E is 200 units. Product A & B both undergo a special manufacturing Process A that has a gross capacity of 450 units (.e. A & B Units put together). By the same token, Products C & D go through a Process B that has a gross capacity of 290 units. Formulate an LP model that will optimize contribution for the company RHS Maximize Minimize Objective Raw Material 1 Raw Material 2 Demand A Demand B Demand C Demand D Committed E Process A Process B

Explanation / Answer

Max. Z = 12A + 18B + 9C + 11D + 4E
Subject to,
2A + 3B + 2C + 2D + 1E <= 1000 (RM 1)
3A + 5B + 4C + 3D + 3E <= 2000 (RM 2)
A <= 400 (Demand A)
B <= 500 (Demand B)
C <= 300 (Demand C)
D <= 280 (Demand D)
E = 200 (Committed E)
A + B <= 450 (Process A)
C + D <= 290 (Process B)
A, B, C, D, E >= 0

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Maximize A B C D E RHS Objective 12 18 9 11 4 Raw mat. 1 2 3 2 2 1 <= 1000 Raw mat. 2 3 5 4 3 3 <= 2000 Demand A 1 0 0 0 0 <= 400 Demand B 0 1 0 0 0 <= 500 Demand C 0 0 1 0 0 <= 300 Demand D 0 0 0 1 0 <= 280 Committed E 0 0 0 0 1 = 200 Process A 1 1 0 0 0 <= 450 Process B 0 0 1 1 0 <= 290

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