A machine shop makes two products. Each unit of the first product requires 3 hours on machine 1 and 2 hours on machine 2. Each unit of the second product requires 2 hours on machine 1 and 3 hours on machine 2. Machine 1 is available only 8 hours per day and machine 2 only 7 hours per day. The profit per unit sold is 16 for the first product and 10 for the second. The amount of each product produced per day must be an integral multiple of 0.25. The objective is to determine the mix of production quantities that will maximize profit.
(a) Formulate an IP model for this problem.
(b) Solve this model graphically.
(c) Use graphical analysis to apply the MIP branch-and-bound algorithm presented in Sec. 12.7 to solve this model.
(d) Now use the interactive procedure for this algorithm in your IOR Tutorial to solve this model.
(e) Check your answers in parts (b), (c), and (d) by using an automatic procedure to solve the model.