Algebra II Story Problem: Please Help!

Question

A manufacturer produces two models of toy airplanes. It takes the manufacturer 20

 minutes to assemble model A and 10

 minutes to package it. It takes the manufacturer  25

 minutes to assemble model B and 5

 minutes to package it. In a given week, the total available time for assembling is 3000

 minutes, and the total available time for packaging is 1200

 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

Let A be the number of units of A that can be produced per week. Let B be the number of units of B that can be produced per week.

20A + 25B = 3000 is the number of both for assembly. 10A + 25B = 1200. Solving simultaneously, A = 100, B = 40. The total profit would be $1320 if both were made. If only A was made, the equation would be 30A = 4200 or 140 units of A which would give $1400 profit. Making only B also gives 140 units for a profit of $1120. It looks like only A should be made to maximize profit.