Solving Systems of Inequalities

1. Your Student Government Association decided to do fundraiser to raise money for a field trip. They decide to sell t-shirts and sweatshirts. The profit for each t-shirt is $10 and the profit for each sweatshirt is $15. They want to sell 50 items at most. Compared to t-shirts, they want to sell at least half as many sweatshirts, with a profit of at least $500.

a. Find a system of inequalities that represents this situation.

b. Graph the system of inequalities.

c. What are the boundaries of the feasible region (i.e. the points that define

the region of solutions)? (Hint: There should be four points)

d. Are there any non-viable solutions within the feasible region?

e. How many t-shirts and sweatshirts should they sell to maximize their profit?

f. What is the maximum profit they can make?