A manufacturer of bicycles builds racing, touring, and mountain models. The bicycles are made of both steel and aluminum. The company has available 71,400 units of steel and 26,400 units of aluminum. The racing, touring, and mountain models need 17,21, and 34 units of steel, and 9,15,12 units of aluminum, respectively. Complete Part A through C below

A) How many of each type of bicycle should be made in order to maximize profit if the company makes $9 per racing bike, $13 per touring bike, and $24 per mountain bike? Let x1 be the number of racing bikes, let x2 be the number of touring bikes, and x3 be the number of mountain bikes. What is the objective function? z= ___ x1 +____x2 +_____x3 ( do not include the $ symbol in your answer)

B) What is the maximum possible profit? $_______. (simplify your answer)

C) Does it require all of the available units of steel and aluminum to build the bicycles that produce maximum profit? If not, how much of each material is left over? Compare any leftover to the value of the relevant slack variable. - A. No since s1=___ and s2=___ in the optimal solution, there is/are ____ units of steel and _____ units of aluminum, respectively, left over OR. - B. Yes, all available units of steel and aluminum are required to build the optimal group of bicycles.