A local manufacturing firm produces four different metal products, each of
which must be machined, polished and assembled. The specific time
requirements (in hours) for each product are as follows:
Machining,
hours
Polishing, hours Assembling,
hours
Product I 3 1 2
Product II 2 1 1
Product III 2 2 2
Product IV 4 3 1
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.