I really need help understanding how to formulate into a LP. here is one of the problems i'm struggling with:
A company makes three different products: product A; product B; product C. Each product requires a piece of metal of the size:
∙ 90cm×3m for product A;
∙ 70cm×3m for product B; and
∙ 50cm×3m for product C.
The company receives metal sheets with size 2m×3m, which needs to be cut into smaller
pieces above. A large order has come in and the company needs to make at least
∙ 300 pieces of product A;
∙ 400 pieces of product B; and
∙ 1000 pieces of product C.
The company wants to find out how to cut up the metal sheets so as to minimize waste.
(a) There are 6 ways to cut a 2m×3m metal sheet into pieces of sizes 90cm×3m, 70cm×3m and 50cm×3m with a waste having the shorter side smaller than 50cm (so that no other pieces can cut out of the waste). What are they and how much metal does each one waste (list them in the order of most waste to least)?
(b) Each of the ways of cutting a metal sheet wastes a certain amount of metal. Obviously
we would like to minimize this waste while still producing enough products
A, B and C.
The cutting machine requires that there is some waste left after the
cutting. This leaves only five cutting options. Write this as a linear programming problem.
Hint. Use variables x1, . . . , x5, where xi denotes the number metal sheets cut using option i. Your goal is to satisfy the production requirements while minimizing the waste.
I'd appreciate any help regarding this problem.