Question

A company makes two products in a single plant. It runs this plant for 100 hours each week. Each unit of product A that the company produces consumes two hours of plant capacity, earns the company a contribution of $1000, and causes, as undesirable side effects, the emission of 4 ounces of particulates. Each unit of product B that the company produces consumes one hour of capacity earns the company a contribution of $2000, and causes, as undesirable side effects, the emission of 3 ounces of particulates and 1 ounce of chemicals. The EPA (Environmental Protection Agency) requires the company to limit the particulate emission to at most 240 ounces per week and chemical emission to at most 60 ounces per week. Solve the problem in Excel and answer the following. The management wants to reduce the number of hours that the plant operates by 10 hours per week. By how much will the plant's profit drop if the management's decision is adopted

Answer 1

Answer:

Check the explanation

Explanation:

As per current limitation of emission, below will be the optimal solution.

The first attached image below is the screenshot of LP Table to be used to get the result -

The second attached image below is the formula used to get the result -

The third attached image below is the screenshot of solver with constraints, decision variable and objective -

the result is in the fourth attached image;

Product A - 15 units

Product B - 60 units

Total Contribution - 135000

Now EPA has allowed one additional unit of chemical emission. Hence, we will change the available quantity of chemical emission to 61 from 60. Rest all will be same as mentioned in earlier part. The fifth attached image below will be the updated optimal solution -

From the image, it is clear that company has 1 additional unit of particulate emission left (240-239), hence company can reduce the particulate emission by 1 units. Below will be the optimal solution -

Product A - 14

Product B - 61

Contribution - 136000 (increase in contribution by 1000)

Now, we can see that contribution has increased by 1000 which is equal to the contribution of 1 unit of product A.

1 unit of Product A is responsible for 4 unit of particulate emission. Hence company can reduce the emission further 4 units.

Final output will be as follows -

Product A - 13

Product B - 61

Contribution - 135000

Total Particulate Emission used = 13*4 + 61*3 = 235

Total Reduction in Particulate Emission = 240-235 = 5 units

Hence, company should willing to reduce the Particulate Emission by 5 units without affecting its Contribution Maximization objective.