In: Operations Management
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.
Which constraint(s) would be best to use for this
statement: “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.”
A. 50,000 ≤ X1 + X2 ≤ 70,000
B. 50,000 ≤ X1 + X2 and X1 + X2 ≤ 70,000
C. X1 + X2 ≥ 50,000 and X1 + X2 ≤ 70,000
D. 50,000 ≥ X1 + X2 ≤ 70,000
E. Any of A, B, or C
Answer : E : Any of A, B, or C
We know that X1= Standard monitors, X2 = Premium monitors
It is required that 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. Thus in other words X1+X2 50000 and X1+X2 70000. Hence option C is correct.
We can now combine both these statement as following 70000 X1+X2 50000 or 50000 X1+X2 70000. Hence option A is correct.
We can also interchange the LHS and RHS in the following X1+X2 50000 and reverse the inequality sign so that it becomes 50000 X1+X2. We already have X1+X2 70000. Hence option B is also correct.
Thus option A, B and C are all valid and correct. Hence option E is correct.