A manufacturer of bicycles builds​ racing, touring, and mountain models. The bicycles are made of both steel and aluminum. The company has available 64,600 units of steel and 24, 000 units of aluminum. The​ racing, touring, and mountain models need 17​, 19​, and 34 units of​ steel, and 9​, 21​, and 12 units of​ aluminum, respectively. Complete parts​ (a) through​ (d) below.

a. Set up the Linear Programming problem is x= # of racing bikes, y=# of touring bikes and z = # of mountain bikes

b. How many of each type of bicycle should be made in order to maximize profit if the company makes $8 per racing bike, $12 per touring bike, and $22 per mountain bike?

c. What is the maximum possible profit?

d. Are there any units of steel or aluminum leftover? How much?