Question

Consider the following linear programming problem

Maximize	$4X1 + $5X2
Subject To	2X1 + 5X2 ≤ 40 hr	Constraint A
	3X1 + 3X2 ≤ 30 hr	Constraint B
	X1, X2 ≥ 0	Constraint C

if A and B are the two binding constraints.

(Round to ONLY two digits after decimal points)

a) What is the range of optimality of the objective function?

  .......... ≤ C1/C2  ≤  ............

b) Suppose that the unit revenues for X1 and X2 are changed to $100 and $18, respectively. Will the current optimum remain the same?

............... that because the new C1/C2 is ........... which is .............. the range of optimality

c) Suppose that the unit revenue of X1 is fixed $4. What is the associated range for the unit revenue for X2 that will keep the optimum unchanged?

   .......... ≤ C2 ≤  ............

d) The Shadow Price for Constraint A is ..........

e) The Shadow Price for Constraint B is .........

f) If only the capacity of Constraint A is increased from the present 40 hours to 45 hours, The increase in revenue will be = $..........

g) A suggestion is made to increase the capacities of Constraint A and B by an hour at the additional cost of $1/hr. Is this advisable?

This is advisable for .............. and the total additional net revenue per hour would be $............

Answer 1