Need help with a b and c Thanks in advacne A large sporting goods store is placi
ID: 3309410 • Letter: N
Question
Need help with a b and c
Thanks in advacne
A large sporting goods store is placing an order for bicycles with its supplier. Four models can be ordered: the adult Open Trail, the adult Cityscape, the girl's Sea Sprite, and the boy's Trail Blazer. It is assumed that every bike ordered will be sold, and their profits, respectively, are 40, 28, 25, and 21. The LP model should maximize profit. There are several conditions that the store needs to worry about. One of these is space to hold the inventory. An adult's bike needs two feet, but a child's bike needs only one foot. The store has 500 feet of space. There are 1200 hours of assembly time available. The child's bike need 4 hours of assembly time; the Open Trail needs 5 hours and the Cityscape needs 7 hours. The store would like to place an order for at least 275 bikes. a. Formulate a linear programming m odel assume X1=the number of the adult Open Train bike ordered X2=the number of the adult Cityscape bike ordered X3=the number of the girl's Sea Sprite bike ordered X4=the number of the boy's Trail Blazer bike ordered b. Solve your linear programming model in part a, using EXCEL Solver, and interpret the results. In other words, how many of each kind of bike should be ordered and what will be the maximum profit? Explain What would be the optimal (maximum) profit be if the store had 120 more feet of storage space? Explain Justify your answer based on your sensitivity report. c.Explanation / Answer
a)Number of bikes=X1+X2+X3+X4
Total assembly time=4*(X3+X4)+5X1+7X2
Total Profit=40X1+28X2+25X3+21X4
Space required=2*(X1+X2)+X3+X4
Now we need to maximise total profit subject to the contraints:
Space<=500
Total bikes>=275
Total assembly time<=1200
b)Maximising the objective function gives: X1=100,X3=175,X2=X4=0
Max Profit=8375
c)If the store had 120ft extra space, Total space<=620ft
Optimizing the solution gives:
X1=100,X3=175,X2=X4=0, Profit=8375
This is because, both the total number of bikes and assembly time have reached the limit and we still have a lot of storage left. The amount of storage required in the current situation is 245ft. This is half of the initial space provided.