King City Inc. manufactures machine tools. The production planner who oversees the production of two of King City’s machines needs to determine how many of each to produce this month. The two machines, TopLathe and BigPress, each require a certain common component. Each TopLathe requires 10 of these components and each BigPress requires 7.

Only 49 components are available this month. The sales department requires that the total number of machines produced in a month must be at least 5 (the number TopLathes plus the number BigPresses must be at least 5). The profit for a TopLathe is \($50,000\) and \($34,000\) for a BigPress.

a. Assuming that adequate labor and all other resources are available, formulate an integer programming model to determine how many of each product King City should produce to maximize profit.

b. Solve the model formulated in part (a) without integer requirements. What is the optimal profit? What are the optimal values for TopLathe and BigPress?

c. Round the TopLathe and BigPress values found in part (b). Is the solution feasible? Why?

d. Truncate the TopLathe and BigPress values found in part (b) (drop the fractional part of each value). Is the solution feasible? Why?

e. Add integer requirements to the model you constructed in part (b). What is the optimal profit and what are the optimal number of TopLathes and BigPresses?