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 31, 25, 21, 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 550 feet of space. There are 1400 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 325 bikes.

The LP for this problem is the following.

MAX 31 X1 + 25 X2 + 21 X3 + 20 X4

SUBJECT TO

2) 2 X1 + 2 X2 + X3 + X4 <= 550

3) 5 X1 + 6 X2 + 4 X3 + 4 X4 <= 1400

4) X1 + X2 + X3 + X4 >= 325

Global optimal solution found.

Objective value: 7825.000

Variable Value Reduced Cost

X1 100.0000 0.000000

X2 0.000000 16.00000

X3 225.0000 0.000000

X4 0.000000 1.000000

Row Slack or Surplus Dual Price

1 7825.000 1.000000

2 125.0000 0.000000

3 0.000000 10.00000

4 0.000000 -19.00000

Ranges in which the basis is unchanged:

Objective Coefficient Ranges:

Current Allowable Allowable

Variable Coefficient Increase Decrease

X1 31.00000 INFINITY 4.750000

X2 25.00000 16.00000 INFINITY

X3 21.00000 3.800000 1.000000

X4 20.00000 1.000000 INFINITY

Righthand Side Ranges:

Current Allowable Allowable

Row RHS Increase Decrease

2 550.0000 INFINITY 125.0000

3 1400.000 125.0000 100.0000

4 325.0000 25.00000 41.66667

How many Trail Blazer bikes should be ordered? (round to the nearest integer)