Question

ABC, Inc. makes three types of computer monitors: Standard, Premium, and Deluxe. The profit per monitor for each is $150 for Standard, $190 for Premium, and $285 for Deluxe. For the coming month, the combined production of Standard monitors and Premium monitors must be at least 50,000 but must not exceed 70,000. The production of Deluxe monitors must be at least 30,000. Also, the production of Standard monitors must not exceed the production of Deluxe monitors plus 10,000. The company wishes to maximize its profit. Use as decision variables: X1= Standard monitors, X2 = Premium monitors, and X3 = Deluxe monitors. We want to state the mathematical model for this case in proper form to run on QM for Windows.

Use this information for questions A,B,C. (Commas are shown here for clarity. You would not enter them to QM.)

A). The objective function is

1. maximize Z = 150X1 + 190X2 + 285X3

2. minimize Z = 150X1 + 190X2 + 285X3

3. maximize Z = X1 + X2 + X3

4. minimize Z = X1 + X2 + X3

5. None of the above

B). Which constraint should be used for: “The production of Deluxe monitors must be at least 30,000.”

1. X3 ≤ 30,000

2. 285X3 ≤ 30,000

3. X3 ≥ 30,000

4. 285X3 ≥ 30,000

5. None of the above

C. The nonnegativity constraint for this model would be: X1, X2, X3 ≥ 0. One part of the nonnegativity constraint is redundant (unnecessary) in this case. Which part?
(Choose only A, B or C).

A. X1 ≥ 0 B. X2 ≥ 0 C. X3 ≥ 0

Answer 1

Let X1 =   Production of Standard computer monitor

X2 = Production of Premium computer monitor

X3 = Production of and Deluxe computer monitor

The profit per monitor for each is $150 for Standard, $190 for Premium, and $285 for Deluxe.

Hence the total profit on Production of Standard computer monitor is $150X1

Total profit on Production of Premium computer monitor is $190X2

Total profit on Production of and Deluxe computer monito is $285X3

Hence objective function is to maximize:

Z = $150X1+$190X2+$285X3

b)

constraint should be used for: “The production of Deluxe monitors must be at least 30,000.” is

X3 ≥ 30,000 ,since X3 is the production of Deluxe monitors

C)   is redundant (unnecessary) in this case,since we know that it should be atleast 30,000, so the minimum value it would take is 30,000