Question

Question 9, 10, and 11 are related to a fixed charge problem, in which a fixed charge of $780 is associated with product 1.  The related integral variable X₁and binary variable Y₁are defined as follows:

             X₁= number of units of product 1 to be produced, an integer.

              Y₁= 1 if X₁>=1, and

              Y₁= 0 if X₁=0.

9. What does the expression “780Y₁” mean?  (select one)

            a. The expense of the $780 fixed charge in any case.

            b. The $780 fixed charge is spent if Y₁=1, and it is not spent if Y₁=0.

            c. It is the total cost of producing project 1, including both fixed and variable costs.

10. Write a constraint to represent: “If X₁=0 then Y₁=0, and if X₁>0 then Y₁can be either 0 or 1”.

11. Write a constraint to represent: “X₁>=1 then Y₁=1, and if X₁=0 then Y₁can be either 0 or 1”.

Answer 1

ANSWER:

9).

Option B is correct.

780Y1 = 780*1 = 780 when (Y1= 1) when it is produced, else 780*0 = 0 (Y1=0) when it is not produced.

10).

To represent the given condition: When there is no production the Variable and the fixed costs are 0.

So, when no production is there the production then Y1 = 0 (Binary) and so the variable cost mulitplier is also 0, X1=0

11).

To represent the given condition: When there is production the Variable and the fixed costs are positive (Non zero).

So, when production is there the production then Y1 = 1 (Binary) and so the variable cost mulitplier is also positive, X1>=1

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