Succulent Citrus produces orange juice and orange concentrate. This year the com

Question

Succulent Citrus produces orange juice and orange concentrate. This year the company anticipates a demand of at least 10,000 quarts of orange juice and 500 quarts of orange concentrate. Each quart of orange juice requires 10 oranges, and each quart of concentrate requires 50 oranges. The company also anticipates using at least 150,000 oranges for these products. Each quart of orange juice costs the company 50¢ to produce, and each quart of concentrate costs $2.00 to produce. How many quarts of each product should Succulent Citrus produce to meet the demand and minimize total costs?

Explanation / Answer

Let the quarts of orange juice be x

Let the quarts of orange concentrate be y

So, we need to minimize the cost, i.e. 0.50x + 2y

To the conditions,

(i) x >= 10000

(ii) y >= 500

(iii) 10x + 50y >= 150000

Solving the above linear programming, we get the minimum cost for x = 10000 and y = 1000, i.e. $7000

So the company should produce 10000 quarts of orange juice and 1000 quarts of orange concentrates so as to meet the demand and minimize the cost.

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