Question

The firm has available to it on weekly basis, 480 hours of machining time, 400 hours of polishing time and 400 hours of assembling time. The unit profits on the product are birr 360, birr 240, birr 360 and birr 480, respectively. The firm has a contract with a distributor to provide 50 units of product i, and 100 units of any combination of products ii and iii each week. Through other customers the firm can sell each week as many units of products i, ii and iii as it can produce, but only a maximum of 25 units of product iv. How many units of each product should the firm manufacture each week to meet all contractual obligations and maximize its total profit? make a mathematical model for the given problem. Assume that any unfinished pieces can be finished the following week.

Answer 1

Let x, y, z, and w be the number of units of products i, ii, iii, and iv, respectively, produced each week.

Maximize 360x + 240y + 360z + 480w

Subject to:

x + y + z = 150 (contractual obligation)

w ≤ 25 (maximum of 25 units of product iv)

x ≤ 480 (available machining time)

y ≤ 400 (available polishing time)

z ≤ 400 (available assembling time)

x, y, z, w ≥ 0 (non-negativity)

The optimal solution is x = 150, y = 0, z = 0, and w = 25, which yields a maximum profit of 90,000 birr.