Problema Solution
A company produces two products, A and B. Each unit of A requires 4 hours on one machine and 5 hours on a second machine. Each unit of B requires 3 hours on the first machine and 2 hours on the second. There are 120 hours available per week on the first machine and 150 hours on the second machine. If the company makes a profit of $85 on each unit of A and $75 on each unit of B, express this as a linear opimization problem in order to maximize the total profit.
Answer provided by our tutors
suppose x is the number of product A
so A cost 4x in first machine cost 5x in second machine
so there still left (120-4x)h for product B in first machine (150-5x) in second machine
so can produce 4(30-x)/3 or 5(30-x)/2
(4（30-x）/3)/(5(30-x)/2) <1
so product can produce 4(30-x)/3
suppose y is maximize the total profit.
so y = 85x + 4(30-x)/3
3y = 215x + 120