Product
I
Product
II
Product
III
Machining, Polishing, hours
hours
3
2
2
4
1
1
2
3
Assembling,
hours
2
1
2
1
Product
IV
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.