Algebra 2 Question

Question

A manufacturer produces two models of toy airplanes. It takes the manufacturer 32 minutes to assemble model A and 8 minutes to package it. It takes the manufacturer 20 minutes to assemble model B and 10 minutes to package it. In a given week, the total available time for assembling is 3200 minutes, and the total available time for packaging is 960 minutes. Model A earns a profit of $10 for each unit sold and model B earns a profit of $8 for each unit sold. Assuming the manufacturer is able to sell as many models as it makes, how many units of each model should be produced to maximize the profit for the given week?

Answer 1

so you will create a few equations based on the information given (by topic).

1. Bounded by (hours): Assembly hours≤ 3200, Packaging hours ≤960
2. Assembly time (subject to above boundary):
3. 32A + 20B ≤ 3200
4. Packaging time (subject to above boundary):
5. 8A + 10B ≤960
6. Maximize this profit equation: P = 10X + 8Y
7. so you can use Desmos graphing calculator (on line) to see what the vertices are to be tested in the Profit equation. You will see the shaded region and the following test points (x,y): (0,0), (0,96), (80,32) and (100,0). Put these values in to the P= 10X +8Y above and see which coordinate maximizes profits:
8. you will discover (80,32) maximizes profits at $1,056; so make 80 model A toys and 32 model B toys to stay within the parameters given and maximize profit.

I hope this process makes sense to you and you are able to carry the concept forward in similar problems.