Question

5.
A small toy company makes only cars and trucks. The profit made on cars is $2 each and the profit made on trucks is $3 each. To stay in business, the company must make at least $500 profit each week. The company only has the resources to make up 200 total cars and trucks each week.

a) Write a system of inequalities that represent possible combinations of toys that the company can make and the amount of profit they will earn. Be sure to define your variables.

b) Can they stay in business? If so, how? (provide evidence)

Answer 1

ALet's call c the number of cars made and t the number of trucks made.
We know that they can make no more than 200 toys a week. This means that $c+t \leq 200$
We know that the cars yield a profit of $2 so the money made from cars is 2c and that the profit for trucks is $3 so the profit for trucks is 3t. Adding these gives the profit which must be 500 or more. That is,$2c+3t \geq 500$
BThey can indeed stay in business. Since they can produce 200 toys, they can produce 100 cars and 100 trucks. 100 cars will yield a profit of (100)(2) = 200. The 100 trucks will yield a profit of (100)(3). Together that is a profit of 200+300=500 which is the minimum needed to stay in business.