A large sporting goods store is placing an order for bicycles with its supplier Four models can be ordered X1, X2, X3, and X4 It is assumed that every bike ordered will be sold, and their unit profits are 30, 25, 22, and 20, respectively The store wants to maximize overall profit, while it needs to worry about several conditions One of these is space to hold the inventory as X1 and X2 bikes need two feet each, but X3 and X4 bikes need only one foot of space each The store has 500 feet of space There are 1200 hours of assembly time available X3 and X4 bikes need 4 hours of assembly time each, X1 needs 5 hours, and X2 needs 6 hours The store would like to place an order for at least 275 bikes A computer solution for this problem is given below OBJECTIVE FUNCTION VALUE 1)6850 0000 VARIABLE VALUE REDUCED COST X1 100 000000 0 000000 X2 0 000000 13 000000 X3 175 000000 0 000000 X4 0 000000 2 000000 ROW SLACK OR SURPLUS DUAL PRICE 2) 125 000000 0 000000 3) 0 000000 8 000000 4) 0 000000 10 000000 NO ITERATIONS 2 RANGES IN WHICH THE BASIS IS UNCHANGED OBJ COEFFICIENT RANGES VARIABLE CURRENT COEFFICIENT ALLOWABLE INCREASE ALLOWABLE DECREASE X1 30 000000 INFINITY 2 500000 X2 25 000000 13 000000 INFINITY X3 22 000000 2 000000 2 000000 X4 20 000000 2 000000 INFINITY RIGHTHAND SIDE RANGES ROW CURRENT RHS ALLOWABLE INCREASE ALLOWABLE DECREASE 2 500 000000 INFINITY 125 000000 3 1200 000000 125 000000 100 000000 4 275 000000 25 000000 35 000000 a Formulate a linear programming equation model for this problem b How many of each kind of bike should be ordered, and what will the profit be c What would the profit be if the store had 100 more feet of storage space Explain why d If the profit on X2 increases to 35, does it make sense to order more X2 bikes Why e Over what range of assembly hours is the dual price applicable Explain the values f If 5 more bikes are required in inventory, what will happen to the optimal solution g Which resource should the company increase first to obtain larger profit and why

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A large sporting goods store is placing an order for bicycles with its supplier. Four models can be ordered: X1, X2, X3, and X4. It

A large sporting goods store is placing an order for bicycles with its supplier. Four models can be ordered: X1, X2, X3, and X4. It is assumed that every bike ordered will be sold, and their unit profits are 30, 25, 22, and 20, respectively. The store wants to maximize overall profit, while it needs to worry about several conditions. One of these is space to hold the inventory as X1 and X2 bikes need two feet each, but X3 and X4 bikes need only one foot of space each. The store has 500 feet of space. There are 1200 hours of assembly time available. X3 and X4 bikes need 4 hours of assembly time each, X1 needs 5 hours, and X2 needs 6 hours. The store would like to place an order for at least 275 bikes.

A computer solution for this problem is given below.

OBJECTIVE FUNCTION VALUE
	1)6850.0000
VARIABLE	VALUE	REDUCED COST
X1	100.000000	0.000000
X2	0.000000	13.000000
X3	175.000000	0.000000
X4	0.000000	2.000000

ROW	SLACK OR SURPLUS	DUAL PRICE
2)	125.000000	0.000000
3)	0.000000	8.000000
4)	0.000000	10.000000

NO. ITERATIONS= 2

RANGES IN WHICH THE BASIS IS UNCHANGED:
		OBJ. COEFFICIENT RANGES
VARIABLE	CURRENT COEFFICIENT	ALLOWABLE INCREASE	ALLOWABLE DECREASE
X1	30.000000	INFINITY	2.500000
X2	25.000000	13.000000	INFINITY
X3	22.000000	2.000000	2.000000
X4	20.000000	2.000000	INFINITY

		RIGHTHAND SIDE RANGES
ROW	CURRENT RHS	ALLOWABLE INCREASE	ALLOWABLE DECREASE
2	500.000000	INFINITY	125.000000
3	1200.000000	125.000000	100.000000
4	275.000000	25.000000	35.000000

a.	Formulate a linear programming equation model for this problem.
b.	How many of each kind of bike should be ordered, and what will the profit be?
c.	What would the profit be if the store had 100 more feet of storage space? Explain why.
d.	If the profit on X2 increases to 35, does it make sense to order more X2 bikes? Why?
e.	Over what range of assembly hours is the dual price applicable? Explain the values.
f.	If 5 more bikes are required in inventory, what will happen to the optimal solution?
g.	Which resource should the company increase first to obtain larger profit and why?