1. A production process can make either four units per hour of product 1 or five units per hour of product 2 or any combination of the two products. If X1 equals the number of units of product 1 and X2 equals the number of units of product 2 to produce, and there are only eight hours of production time available, then this requirement can best be expressed by:

A. 4 X1 + 5 X2 >= 8

B. (1/4) X1 + (1/5) X2 <= 8

C. 4 X1 + 5 X2 <= 8

D. (1/4) X1 + (1/5) x2 <= (1/8)

E. None of the above

2. A negative shadow price means that an increase of one unit in the right-hand side will:

A. Decrease the optimal value of the objective function, but only if it is a maximization problem.

B. Increase the optimal value of the objective function, but only if it is a minimization problem.

C. Both a and b.

D. Decrease the optimal value of the objective function regardless of whether it is a maximization or minimization problem.

E. None of the above

3. In LP, if a constraint is non-binding, then the following is true:

A. it does not pass through the optimal corner point.

B. if it is a <= constraint, there will always be a non-negative slack.

C. if it is a >= constraint, there will be a non-negative surplus.

D. all of the above.

E. None of the above.