Question

Solve the following LP problem using the Solver in MS Excel.  

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

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:

Using following constraints in solver:

The solver out put obtained from this is:

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