1. manufactures special and ordinary pendant lights. Every special pendant light requires 12 pounds of brass while each ordinary pendant light requires 6 pounds of brass. The company's brass supply is limited to 960 pounds during each production period. Each special type requires 9 hours of assembly time in the machine and each ordinary type requires 3 hours of assembly time in the machine. The company's assembly machines are available only for 540 hours in each production period.Each special type requires 7 light bulbs that must be imported from Taiwan. The importation of these bulbs is limited to 300 units. The contribution to profit of each special pendant light is P3300 and P1575 on the ordinary pendant light.

The following is the Linear Programming Model:

Maximize Profit = 3300 X₁+ 1575X₂

Subject to: 12X₁ + 6X₂ 960 (pound of brass)

9X₁ + 3X₂ 540 (assembly hours)

7X₁ 300 (importation)

X₁; X₂ 0

Optimal Solution

Cj	3300	1575	0	0	0
Ci	Solution		X1	X2	S1	S2	S3
0	S3	160	0	0	1.1667	-2.33	1
1575	X2	120	0	1	0.5	-0.66	0
3300	X1	20	1	0	-0.1667	0.333	0
	Zj	255,000	3300	1575	237.5	50	0
Cj-Zj	0	0	-237.5	-50	0

Sensitivity (Post Optimality) Solution

Range of Optimality
OF Variable	Minimum Value	Original Value	Maximum Value
X1	3150	3300	4725
X2	1100	1575	1650
Range of Feasibility
RHV	Minimum Value	Original Value	Maximum Value
q1	822.86	960	1080
q2	480	540	608.57
q3	140	300	+

1. Determine the quantity of special and ordinary pendant light that must be produced and determine also the expected maximum profit. (5 points)
2. Based on the optimal solution presented, analyze if there will be slack or surplus resource. Interpret your answer. (10 points)
3. Suppose that the profit contribution of special pendant light is increased from P3300 to P4000 and the profit contribution of ordinary pendant light is reduced from P1575 to P1337, what effect would this change have on the optimal production quantity and the total profit. Explain your answer. (10 points)
4. Determine the cost per pound of brass, and the cost per hour of assembly machine to minimize the cost. Analyze and explain if the production cost will change if the available brass is reduced by 70 pounds, and the assembly machine hours is increased by 30 hours. (15 points)
5. Up to what extent should the capacity of the individual resource have to be increased or decreased without sacrificing the total production cost? Explain your answer. (10 points)