what is linear programming? math problem?

Question

a manufacturer of two models of wok has determined that the profit from work A is $15 and the profit for B is $20. the manufacturer can produce no more than 200 woks per week. to meet the market demand, at least 50 wok A must be made and 100 of Wok B must be available for sale each week. find the number of woks A and B that would lead to the maximum profit

Answer 1

In this case, since the marginal profit is positive and constant on both types, and there are no differences stated in the amount of resources required for producing the different types, we can assume that we will produce the maximum possible number of woks, and indeed that we will produce as many wok Bs as possible. So it's clearly 50 wok As and 150 wok Bs.

In the linear programming approach you'd set up your constraints (x >= 50, y >= 100, x + y <= 200), find the corners of the feasible region (at (50, 100), (50, 150) and (100, 100)) and set up an objective function 15x + 20y to be maximised. And you'd find, unsurprisingly, that the corner at (50, 150) gives the maximum value. But in this case it doesn't seem worth doing all that work.