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 30,000 units of aluminum. The​ racing, touring, and mountain models need 17​, 19​, and 34 units of​ steel, and 9​, 18​, and 15 units of​ aluminum, respectively. Required:
a. How many of each type of bicycle should be made in order to maximize profit if the company makes $8 per racing bike?
b. What is the maximum possible profit ?
c. Does it require all of the available unit s of steel and aluminum to build the bicycles that produce the maximum profit? If not, how much of each material is left over? Compare any leftover to the value of the relevant slack variable.
d. There are many unstated assumptions in the problem given above. Even if the mathematical solution is to make only one or two types of the bicycles , there may be demand for the type(s) not being made , which would create problems for the company. Discuss this and other difficulties that would arise in a real situation.