Gordy Knotworthy, owner of a small woodworking shop that employs five skilled craftsmen, is planning the shop’s production schedule for next week. The shop manufactures 3 wood products, which it sells to a large sporting goods company: persimmon golf club heads, ash tennis racquet frames, and ash baseball bats. He expects to net $25 for each club head, $30 for each racquet frame, and $10 for each baseball bat produced by the shop. To be feasible, the production schedule must satisfy certain limitations. Next week’s production is limited by the amount of wood stock available. At most, only 120 golf club heads can be made with the persimmon in stock. Additionally, the maximum combined total of 140 racquet frames and bats can be made with the ash in stock. The shop is also limited by the capacity of its dust-free varnishing and finishing room, which cannot process more than 160 units per week. Gordy guarantees his employees at least 40 hours per week for each employee. The five employees are equally skilled in each product. Each golf club head requires 2 hours of production labor. Each racquet requires 1 hour, and each baseball bat requires 30 minutes. Let C = Number of Golf Club Heads to produce R = Number of Tennis Racquets to produce B = Number of Baseball Bats to produce a. Formulate a linear program to use for maximizing profit from next week’s production schedule. b. Use MS Excel / Solver to determine the optimum production schedule for next week. What is the optimum production schedule? Note: Each of the following variations of this problem go back to the original and make one change. The following items are not cumulative; each starts with the original. For each item below, state the optimum solution and resulting profit. c. How would the solution in 2-b change if Gordy only made $5 on each club head? What is the optimum solution and resulting profit? d. How would the solution in 2-b change if there were only 120 units of ash available for next week’s production? What is the optimum solution and resulting profit? e. How would the solution in 2-b change if Gordy could only make $20 on each racquet frame? What is the optimum solution and resulting profit? f. Gordy learns that for a fee of $100 per week, he could rent space in the finishing room of a nearby shop. If Gordy rents the space, he will have room to varnish and finish 10 more total units of finished product. Should Gordy rent the space? Explain. What is the optimum solution and resulting profit? g. Gordy is not obligated to offer any employee more than 40 hours of work each week, but he does guarantee each employee 40 hours worth of wages. He even pays employees who miss a day of work if the worker gets his permission for the absence. Suppose that one of his workers, who earns $12.50 per hour, asks to be excused next Friday. This would reduce the number of hours that Gordy would have to schedule. Based solely on the effect this would have on next week’s profits, should Gordy let his worker have the day off? What is the optimum solution and resulting profit?