Question

A factory can produce two products, x and y, with a profit approximated by P = 14x + 22y – 900. The production of y can exceed x by no more than 100 units. Moreover, production levels are limited by the formula x + 2y ≤ 1,400. What production levels yield maximum profit?

Answer 1

@zaynahf

Answer 2

Ok I think I finally solved this one, and to be honest I despise these types of questions :) but here goes anyways.

With you wanting the maximum profit defined by P=14x+22y-900, which parameter has the maximum effect on profit? Since y is multiplied by 22 you really want to maximize how much y shows up to make much moolah.

Now we move onto x+2y<=1400, again, since we want the max we won't use less that 1400 total.. that would be silly, since what are we looking for? moolah.

Now finding a relationship between x and y was my next step, because I want to find just how much y I can have without going over 1400. The best would just be to use y for the formula, but x is tied to it with a margin of 100, but again we want to minimize x's involvement so we can deduce the following relationship: x=y-100.

Back to x+2y<=1400. Now we can plug in our relationship to just have a single variable equation and solve. y=500 is what we find. Thus, x=400.

I'm quite confident this is correct.

Answer 3

look at image below

Answer 4

That looks really nice, but it far exceeds the limit of 1400<=x+2y

Answer 5

look now

Answer 6

that still exceeds the limit :/

Answer 7

plz write all the limits in math