Fancy Pineapple produces pineapple juice and canned pineapple rings. This year the company anticipates a demand of at least 10,000 pints of pineapple juice and 500 cans of pineapple rings. Each pint of pineapple juice requires 2 pineapples, and each can of pineapple rings requires 1 pineapple. The company anticipates using at least 5,000 pineapples for these products. Each pint of pineapple juice costs the company 20 cents to produce, and each can of pineapple rings costs 50 cents to produce. How many pints of pineapple juice and cans of pineapple rings should Fancy Pineapple produce to meet the demand and minimize total costs ?
A)25,000 pints of pineapple juice and 500 cans of pineapple rings
B) 500 pints of pineapple juice and 10,000 cans of pineapple rings
C) 1,000 pints of pineapple juice and 25,000 cans of pineapple rings
D) 10,000 pints of pineapple juice and 500 cans of pineapple rings
E) 25,000 pints of pineapple juice and 1,000 cans of pineapple rings

Question

Fancy Pineapple produces pineapple juice and canned pineapple rings. This year the company anticipates a demand of at least 10,000 pints of pineapple juice and 500 cans of pineapple rings. Each pint of pineapple juice requires 2 pineapples, and each can of pineapple rings requires 1 pineapple. The company anticipates using at least 5,000 pineapples for these products. Each pint of pineapple juice costs the company 20 cents to produce, and each can of pineapple rings costs 50 cents to produce. How many pints of pineapple juice and cans of pineapple rings should Fancy Pineapple produce to meet the demand and minimize total costs  ?
A)25,000 pints of pineapple juice and 500 cans of pineapple rings
B) 500 pints of pineapple juice and 10,000 cans of pineapple rings
C) 1,000 pints of pineapple juice and 25,000 cans of pineapple rings
D) 10,000 pints of pineapple juice and 500 cans of pineapple rings
E) 25,000 pints of pineapple juice and 1,000 cans of pineapple rings

Quizplus · Accepted Answer

Since the demand is at least 10,000 pints of pineapple juice and 500 cans of pineapple rings, we know that we need to produce at least that much.

We also know that each pint of pineapple juice requires 2 pineapples, and each can of pineapple rings requires 1 pineapple. So, to produce 10,000 pints of juice and 500 cans of rings, we need a total of 20,500 pineapples (10,000 x 2 + 500 x 1).

Since the company anticipates using at least 5,000 pineapples for these products, we know that we have at most 15,500 pineapples available for other products or for waste.

Now we need to determine the cost of producing each product. Each pint of pineapple juice costs 20 cents to produce, and each can of pineapple rings costs 50 cents to produce.

To minimize total costs, we want to produce as many of each product as possible while staying within the limit of 15,500 pineapples.

Let's start by calculating how many pints of juice we can produce with 15,500 pineapples:

15,500 pineapples ÷ 2 pineapples per pint = 7,750 pints of juice

Now let's calculate how many cans of rings we can produce with the remaining pineapples:

15,500 pineapples - (7,750 pints x 2 pineapples per pint) = 0 pineapples left

Uh oh, we don't have any pineapples left to produce cans of rings. This means that we should produce the maximum possible number of pints of juice and no cans of rings.

Therefore, the best choice is D: 10,000 pints of pineapple juice and 500 cans of pineapple rings.

Fancy Pineapple Produces Pineapple Juice and Canned Pineapple Rings