Please answer each of the following questions step-by-step:

Nam Trieu Electronics manufactures two LCD television monitors, identified as model A and model B. Each model has its lowest possible production cost when produced on Nam Trieu's new production line. However the new production line does not have the capacity to handle the total production of both models. As a result, at least some of the production must be routed to a higher-cost, old production line. The following table shows the minimum production requirements for next month, the production line capacities in units per month, and the production cost per unit for each production line.

	Production Cost per Unit		Minimum Production Requirements
Model	New Line	Old Line
A	$19	$7	50,000
B	$15	$47	70,000
Production Line Capacity	80,000	60,000

Let AN = Units of model A produced on the new production line

AO = Units of model A produced on the old production line

BN = Units of model B produced on the new production line

BO = Units of model B produced on the old production line

Nam Trieu's objective is to determine the minimum cost production plan. The sensitivity report is shown below:

Variable Cells

Cell	Name	Final Value	Reduced Cost	Objective Coefficient	Allowable Increase	Allowable Decrease
$B$14	Total Costs AN	0	12	19	1E+30	12
$C$14	Total Costs AO	50000	0	7	12	7
$D$14	Total Costs BN	70000	0	15	32	15
$E$14	Total Costs BO	0	32	47	1E+30	32

Constraints

Cell	Name	Final Value	Shadow Price	Constraints R.H.Side	Allowable Increase	Allowable Decrease
$B$19	Minimun production for A Amount Used	50000	7	50000	10000	50000
$B$20	Minimun production for B Amount Used	70000	15	70000	10000	70000
$B$21	Capacity of new production line Amount Used	70000	0	80000	1E+30	10000
$B$22	Capacity of old production line Amount Used	50000	0	60000	1E+30	10000

a) Formulate the linear programming model for this problem using the following four constraints

Constraint 1: Minimum production for model A

Constraint 2: Minimum production for model B

Constraint 3: Capacity of the new production line

Constraint 4: Capacity of the old production line

b) Using the sensitivity analysis information in table above, what is the optimal solution and what is the total production cost associated with this solution?

c) Which constraints are binding? Explain.

d) The production manager noted that the constraint with a positive shadow price is the constraint on the capacity of the new production line. The manager's interpretation of the shadow price was that one-unit increase in the right-hand-side of this constraint would actually increase the total production cost by $0 per unit. Do you agree with this interpretation? Would an increase in capacity for the new production line be desirable? Explain.

e) Would you recommend increasing the capacity of the old production line? Explain.

f) The production cost for model A on the old production line is $7 per unit. How much would this cost have to change to make it worthwhile to produce model A on the old production line? Explain.

g) Suppose that the minimum production requirement for model B is reduced from 70000 units to 60000 units. What effect would this change have on the total production cost? Explain.