Question

A movie theater manager of a small theater sells two sizes of popcorn at the concession stand. A jumbo popcorn has a profit of $4 and a mini popcorn has a profit of $3. The manager knows the maximum number of popcorn boxes that will fit in the concession stand, the cost of making the popcorn, and the minimum number of boxes he wants to sell each day. Let j represent the number of jumbo popcorns sold and let m represent the number of mini popcorns sold. What is the objective function, and how can it be used to maximize the profit based on the the given conditions?

Answer 1

j4 + m3 = p

If you multiply j, which is the number of jumbo popcorns sold by its price, you are given the profit of the Jumbo boxes for a single day. If you multiply m, which is the number of mini popcorns sold by its price, you are given the profit of the Mini boxes for a single day. If you add the profits from both boxes together... you are given p, which is the total profit for the day.