QUESTION 16

1. 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 30, 25, 22, and 20. The LP model should maximize profit. The store needs to worry about several conditions. 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 bikes need 4 hours of assembly time, the Open Trail needs 5 hours, and the Cityscape needs 6 hours. The store would like to place an order for at least 275 bikes.

   Formulate an LP model for this problem.

   Assume that X₁, X₂, X₃, X₄ are the number of bicycles to be ordered from each category Open Trail, Cityscape, Sea Sprite, and Trail Blazer, respectively.

   A.

   Max	30X1 + 25X2 + 22X3 + 20X4
   Subject to	2X1 + 2X2 + X3 + X4 500
   	5X1 + 6X2 + 4X3 + 4X4 1200
   	X1 + X2 + X3 + X4 275

   B.

   Max	30 X1 + 25 X2 + 22 X3 + 20 X4
   Subject to	2X1 + 2X2 + X3 + X4 500
   	5X1 + 6X2 + 4X3 + 4X4 1200
   	X1 + X2 + X3 + X4 275
   	X1, X2 , X3, X4 0

   C.

   Max	500X1 + 1200X2 + 275X3
   Subject to	2X1 + 2X2 + X3 + X4 30
   	5X1 + 6X2 + 4X3 + 4X4 25
   	X1 + X2 + X3 + X4 22
   	X1 + 2X2 + X3 + 2X4 20

   D.

   Max	30 X1 + 25 X2 + 22 X3 + 20 X4
   Subject to	2X1 + 2X2 + X3 + X4 500
   	5X1 + 6X2 + 4X3 + 4X4 1200
   	X1 + X2 + X3 + X4 275

   E.

   Max	30X1 + 25X2 + 22X3 + 20X4
   Subject to	X1 + X2 + 2X3 + 2X4 500
   	4X1 + 4X2 + 5X3 + 6X4 1200
   	X1 + X2 + X3 + X4 275

2. Solve your model with any computer package available to you. How many of each kind of bike should be ordered, and what will the profit be? (Round your answer to nearest integer if necessary.)

   Order		Open Trails,
   		Cityscapes,
   		Sea Sprites, and
   		Trail Blazers.
   Profit will be $		.