Machine Tool Production Planning. 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$.$ Based on the solution for the LP relaxation model given below, round the TopLathe and

BigPress values. Is the solution feasible? Why?