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? It will stay the same 500 850 1250

IGNORE THE BLUE DOT:

A. It will stay the same

B. 500

C. 850

D.1250

Answer 1

Decision variables:

A = units of product A that the company produces per week

B = units of product B that the company produces per week

Objective Function:

Max 1000 A + 2000 B (profit $/week)

Constraints:

• Restrictions on production

2A + B ≤ 100

• Restrictions on emission

4A + 3B ≤ 240 B ≤ 60

• Nonnegativity constraint on each of the two variables.

A ≥ 0, B ≥ 0

OBJECTIVE FUNCTION VALUE

1) 135000.0

VARIABLE     VALUE REDUCED          COST

       A                 15.000000             0.000000

       B                  60.000000             0.000000

ROW             SLACK OR SURPLUS      DUAL PRICES

2)                         10.000000                 0.000000

3)                          0.000000                250.000000

4)                          0.000000              1250.000000

NO. ITERATIONS= 2

The optimal plan is to produce each week 15 units of product A and 60 units of product B

Reducing the production hour by 10 hours, the plant’s profit will drop by an amount of $1250.

The correct option is D.