Suppose that three water purification facilities can handle at most 18 million gallons in a certain time period. Plant 1 leaves 20% of certain impurities, and costs $20,000 per million gallons. Plant 2 leaves 15% of these impurities and costs $30,000 per million gallons. Plant 3 leaves 10% impurities and costs $40,000 per million gallons. The desired level of impurities in the water from all three plants is at most 15%. If Plant 1 and Plant 3 combined must handle at least 14 million gallons, find the number of gallons each plant should handle so as to achieve the desired level of purity at minimum cost. Find the minimum cost.
A) Minimum cost is $360,000 with plants 1 and 3 each handling 6,000,000 gallons and plant 2 handling 0 gallons.
B) Minimum cost is $480,000 with plants 1 and 3 each handling 7,000,000 gallons and plant 2 handling 4,000,000 gallons.
C) Minimum cost is $540,000 with plants 1 and 3 each handling 8,000,000 gallons and plant 2 handling 2,000,000 gallons.
D) Minimum cost is $480,000 with plants 1 and 3 each handling 8,000,000 gallons and plant 2 handling 0 gallons.
E) Minimum cost is $420,000 with plants 1 and 3 each handling 7,000,000 gallons and plant 2 handling 0 gallons.

Question

Suppose that three water purification facilities can handle at most 18 million gallons in a certain time period. Plant 1 leaves 20% of certain impurities, and costs $20,000 per million gallons. Plant 2 leaves 15% of these impurities and costs $30,000 per million gallons. Plant 3 leaves 10% impurities and costs $40,000 per million gallons. The desired level of impurities in the water from all three plants is at most 15%. If Plant 1 and Plant 3 combined must handle at least 14 million gallons, find the number of gallons each plant should handle so as to achieve the desired level of purity at minimum cost. Find the minimum cost. ​
A) Minimum cost is $360,000 with plants 1 and 3 each handling 6,000,000 gallons and plant 2 handling 0 gallons.
B) Minimum cost is $480,000 with plants 1 and 3 each handling 7,000,000 gallons and plant 2 handling 4,000,000 gallons.
C) Minimum cost is $540,000 with plants 1 and 3 each handling 8,000,000 gallons and plant 2 handling 2,000,000 gallons.
D) Minimum cost is $480,000 with plants 1 and 3 each handling 8,000,000 gallons and plant 2 handling 0 gallons.
E) Minimum cost is $420,000 with plants 1 and 3 each handling 7,000,000 gallons and plant 2 handling 0 gallons.

Quizplus · Accepted Answer

To minimize cost while meeting impurity requirements, Plants 1 and 3 should handle 7 million gallons each, leaving 20% and 10% impurities respectively. This results in an average impurity level of 15%, meeting the requirement. Plant 2 is not needed, minimizing cost to $420,000.

Suppose That Three Water Purification Facilities Can Handle at Most