A manufacturer of bicycles builds racing, touring, and mountain models. The bicycles are made of both steel and aluminum. The company has available 46,800 units of steel and 34,200 units of aluminum. The racing, touring, and mountain models need 13, 18, and 26 units of steel, and 12, 27, and 18 units of aluminum, respectively. Complete parts (a) through (d) below. (a) How many of each type of bicycle should be made in order to maximize profit if the company makes $7 per racing bike, $11 per touring bike, and $20 per mountain bike? Let x be the number of racing bikes, let x be the number touring bikes, and let x3 be the number of mountain bikes. What is the objective function? + Z= (Do not include the $ symbol in your answers.) To maximize profit, the company should produce (Simplify your answers.) (b) What is the maximum possible profit? The maximum profit is $. (Simplify your answer.) racing bike(s), touring bike(s), and mountain bike(s). (c) Does it require all of the available units 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. Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. in the optimal solution, there is/are unit(s) of steel and unit(s) of aluminum, respectively, left over. OA. No. Since s = and S = (Simplify your answers.) B. Yes. All available units of steel and aluminum are required to build the optimal group of bicycles. (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 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. Choose the correct answer below. A. The company may acquire more units of aluminum and steel, which would allow for producing more bicycles. A linear programming model cannot account for this. B. Producing more of one type of bicycle requires producing fewer of another type of bicycle. The linear programming model does not account for this. C. If the manufacturer chooses to satisfy demand for the type(s) of bicycles not being made, the profit will be reduced. D. Due to higher production of certain types of bicycles, the company may incur higher costs for bicycle repairs. This would reduce the profit generated for certain levels of production.