Linear Programming

A machine shop makes two parts, I and II, each requiring the use of three machines, A, B, C. Each Part I requires 4 minutes on Machine A, four minutes on Machine B and five minutes on machine C. Each Part II requires five minutes on Machine A, one minutes on Machine B and six minutes on Machine C. The shop makes a profit of $8 on each Part I and $5 on each Part II. However, the number of units of Part II produced must not be less than half the number of Part I. Also each day the shop has only 120 minutes of machine A, 72 minutes of Machine B, and 180 minutes of Machine C available for the production of the two parts. What should be the daily production of each part to maximize the shop's profit?

please show me to start this problem by showing the variables, constraints, or anything else,please

Hi Jes,

We start by defining variables (this is always the starting point): x is the number of parts of type I made, and y is the number of parts of type II made.

Then the time constraint on machine A is

4x + 5y <= 120 and there are similar time constraints on machines B and C; plus the constraint on the relative number of parts of type I and II made: y >= (  1/2)x, that is, (  1/2)x - y <= 0. You should be able to figure out the profit function that should be maximized by yourself. Then you will have the whole LP problem.

(By the way, there is an online resource at for solving LP problems.)

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