Question

A municipality has two incinerators for burning trash. Incinerator A costs $3 .80 per ton of trash to operate, and has a capacity of 28 tons per day. Incinerator B costs $4 .25 per ton to operate, and has a capacity of 30 tons per day. The municipality produces over 100 tons of trash per day, and all trash not burned in the incinerators must be buried in a land fill at a cost of $5 .00 per ton. The city manager wants to minimize costs by burning as much trash as possible. However, the city must conform to environmental regulations limiting production of pollutants from burning in the incinerators to 180 pounds of hydrocarbons and 640 pounds of particulates a day. Incinerator A produces 3 pounds of hydrocarbons and 20 pounds of particulates for every ton of trash burned, and incinerator B produces 5 pounds of hydrocarbons and 10 pounds of particulates for every ton of trash. Determine the optimum amount of trash to burn in each incinerator.

Answer 1

Answer:

Thus the muncipality should burn 20 tons in incinerator A and 24 tons in Incinerator B.

Explanation:

First of all make the LP equations for the given problem.

Let Xa be the tons of trash burned in incinerator A and Xb be the tons of trash burned in Incinerator B.

Our objective function will be:

Maximize Xa + Xb

Subject to constraints:

Xa <=28

Xb<=30

3Xa + 5Xb<=180

20Xa + 10Xb<=640

Now these equations can be solved in Excel using solver as follows: