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Question

Your Student Government Association decided to do a 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 sellat least half as many sweatshirts, with a profit of at least $500.a. Write a system of inequalities that represents this situation

Answer 1

Looks like a linear programming question, with a maximize objective function.

Let S = quantity of sweatshirts

Let T = quantity of t-shirts

Objective function: Profit = $15*S + $10*T

Subject to the following inequalities:

1. S + T is less than or equal to 50 (they want to sell 50 items at most)
2. S is greater than or equal to 0.5*T (they want to sell at least 1/2 as many sweatshirts)
3. $15*S is greater than or equal to $500 (they want the profit from sweatshirts to be at least $500.

divide each side by $15 to have the following:

S is greater than or equal to 33.33

However, since sweatshirts come in only whole number units:

S is greater than or equal to 34.