Warmups 3.7

Write the system of inequalities and optimum function created by each problem.

1. Abercrombie sells both children and adult clothes.  In one day, the store will sell a maximum of 65 total shirts with the adult shirts selling for $27 and the child shirt selling for $20. The store must sell at least 15 children’s shirts and 10 adult shirts.  How much money will the store make?

2. A land developer wishes to build one-story and two-story houses on his plot of land.  He is allowed to build a maximum of 60 houses on 50 acres of land.  One story houses take .75 acres to build and will sell for $150,000.  Two story houses take 1 acres to build and will sell for $180,000.  The builder must build at least 20 one-story houses and 5 two-story houses as well.  How much will the developer make?

3. John can make at most $2,700 in television and radio sales today.  He knows he will sell exactly 35 radios and televisions.  Also, he knows that he won’t sell more than 30 radios at $70 or 15 televisions at $100.  What is the most he can actually make?