Question 2 Better Products, Inc., manufactures three products on two machines. In a typical week, 40 hours are available on each machine. The profit contribution and production time in hours per unit are as follows:

Category	Product 1	Product 2	Product 3
Profit/unit	$30	$50	$20
Machine 1 time/unit	0.5	2.0	0.75
Machine 2 time/unit	1.0	1.0	0.5

Two operators are required for machine 1; thus, 2 hours of labor must be scheduled for each hour of machine 1 time. Only one operator is required for machine 2. A maximum of 100 laborhours is available for assignment to the machines during the coming week. Other production requirements are that product 1 cannot account for more than 50% of the units produced and that product 3 must account for at least 20% of the units produced. Answer the following questions (a-i) using the output below and where necessary a range analysis must be shown. a) What is the optimal solution ( in words? (2 marks) b) Five (5) hours of machine 1 were lost due to repairs. Evaluate the effect? Explain-( 3 marks) c) An additional seven hours of machine 2 became available. Evaluate the effect? (3 marks) d) An additional 20 hours of labour became available. Evaluate the effect(2 -marks e) The profit per unit for product 2 decreased by $5.Evaluate the effect (3 marks) f) What are the allowable values within which maximum production for product 1 vary without affecting the shadow price?- (2 marks) g) Is the problem degenerate? Explain! (2 marks) h) Are there alternative optima in this problem? Explain (2 marks) i) What value should be in the slack column that is given by ???? (1 mark)

Number of units	24	8	16
Profit	30	50	20	1440

Constraints

Machine 1	0.5	2	0.75	40	<=	40
Machine 2	1	1	0.5	40	<=	40
Labor hrs	1	1	1	48	<=	100
Max product 1	0.5	-0.5	-0.5	0	<=	0
Min product 3	-0.2	-0.2	0.8	6.4	<=	0
				LHS	SIGN	RHS