Question

A grocery store manager must decide how to best present a limited supply of milk and cookies to its customers. Milk can be sold by itself for a profit of $1.50 per gallon. Cookies can likewise be sold at a profit of $2.50 per dozen. To increase appeal to customers, one gallon of milk and a dozen cookies can be packaged together and sold for a profit of $3.00 per bundle. The manager has at most 100 gallons of milk and 150 dozen cookies to make available each day. The manager has decided to stock at least 75 individual gallons of milk per day (excluding milk bundled with cookies). Demand for individual packages of cookies is at most 140 dozen per day (excluding cookies bundled with milk). The manager wishes to determine how much of each product to stock each day. Which of the following is the constraint that limits the amount of milk the store will use (both in bundles and sold separately) each day?

Answer 1

The constraint limits the total milk usage to 100 gallons per day, reserving at least 75 gallons for individual sale, leaving at most 25 gallons for bundling with cookies.

Step-by-step explanation:

The constraint that limits the amount of milk the store will use each day is the maximum supply of milk available to the store manager, which is 100 gallons. The manager wants to ensure that at least 75 gallons of milk (excluding the milk bundled with cookies) are available for individual sale every day. Therefore, the milk used for bundling with cookies must not exceed the remaining 25 gallons after setting aside 75 gallons for individual sale. This gives us the inequality representing the milk constraint:

Individual milk gallons + Bundled milk gallons ≤ 100 gallons

In other words, the total amount of milk (individual plus bundled) cannot exceed 100 gallons, keeping in mind that the individual milk gallons must be at least 75 gallons. Thus, we have:

75 gallons + Bundled milk gallons ≤ 100 gallons

Hence, the bundled milk gallons can be at most 25 gallons in order to meet the described constraint.