# Question

Vincent Cardoza is the owner and manager of a machine shop that does custom order work. This Wednesday afternoon, he has received calls from two customers who would like to place rush orders. One is a trailer hitch company which would like some custom-made heavy-duty tow bars. The other is a mini-car-carrier company which needs some customized stabilizer bars. Both customers would like as many as possible by the end of the week (two working days). Since both products would require the use of the same two machines, Vincent needs to decide and inform the customers this afternoon about how many of each product he will agree to make over the next two days.

Each tow bar requires 3.2 hours on machine 1 and 2 hours on machine 2. Each stabilizer bar requires 2.4 hours on machine 1 and 3 hours on machine 2. Machine 1 will be available for 16 hours over the next two days and machine 2 will be available for 15 hours. The profit for each tow bar produced would be $130 and the profit for each stabilizer bar produced would be $150.

Vincent now wants to determine the mix of these production quantities that will maximize the total profit.

(a) Formulate an IP model for this problem.

(b) Use a graphical approach to solve this model.

(c) Use the computer to solve the model.

Each tow bar requires 3.2 hours on machine 1 and 2 hours on machine 2. Each stabilizer bar requires 2.4 hours on machine 1 and 3 hours on machine 2. Machine 1 will be available for 16 hours over the next two days and machine 2 will be available for 15 hours. The profit for each tow bar produced would be $130 and the profit for each stabilizer bar produced would be $150.

Vincent now wants to determine the mix of these production quantities that will maximize the total profit.

(a) Formulate an IP model for this problem.

(b) Use a graphical approach to solve this model.

(c) Use the computer to solve the model.

## Answer to relevant Questions

Consider the following BIP problem: Maximize Subject to and all xj binary. Consider the problem of assigning swimmers to the different legs of a medley relay team that is presented in Prob. 9.3-4. The answer in the back of the book shows the formulation of this problem as an assignment problem. Use ...Poor inventory management at the local warehouse for Furniture City has led to overstocking of many items and frequent shortages of some others. To begin to rectify this situation, the 20 most popular kitchen sets in ...Consider the variation of the Wyndor Glass Co. example represented in Fig. 13.5, where the second and third functional constraints of the original problem (see Sec. 3.1) have been replaced by 9x12 + 5x22 ≤ 216. Demonstrate ...Use the bisection method with an error tolerance ϵ = 0.04 and with the following initial bounds to interactively solve (approximately) each of the following problems. (a) Maximize f(x) = 6x – x2, with x = 0, x-bar = ...Post your question

0