Mathematics
OpenStudy (anonymous):

A company manufactures two products, A and B, in 2 factories, I and II. It has been determined that the company will realize a profit of 50 dollars on each unit of product A and a profit of 53 dollars on each unit of product B. To manufacture a unit of product A requires 4 minutes in factory I and 10 minutes in factory II. To manufacture a unit of product B requires 7 minutes in factory I and 6 minutes in factory II. There are 350 minutes of machine time available in factory I and 530 minutes of machine time available in factory II per day. How many units of each product should be produced

OpenStudy (anonymous):

per day to maximize the company's profit? What is the maximum achievable profit per day? Now assume that, due to changing market conditions, the company can now realize a profit of 91 dollars on each unit of product A, whereas the profit on product B remains the same as before. How many units of each product should now be produced per day to maximize the company's profit? What is the maximum achievable profit per day?

OpenStudy (dumbcow):

4A +7B < 350 --> B < 50 -(4/7)A 10A +6B < 530 --> B< 88.3 -(5/3)A P = 50A +53B max profit occurs where 2 lines intersect 50-4/7A = 88.3 -5/3A 23/21A = 38.3 A = 35 -> B = 30 maxP = 3340

OpenStudy (dumbcow):

For next part change profit equation to : P = 91A +53B

OpenStudy (anonymous):

When you solved for A and B, you didn't use the profit equation. So how can I find different values for A and B through a different equation?

OpenStudy (dumbcow):

graph the 2 lines |dw:1331698861357:dw| profit will be maximized at one of the 3 endpoints depending on the profit equation if profit is weighted relatively evenly then the intersection is usually most profitable however, if either A or B extremely outweighs the other then its most profitable to only produce the 1 product. such as when P = 91A +53B, A is just valuable enough now that you are better off when B=0 --> 91*53 = 4823 --> 91*35 +53*30 = 4775