4-28The Classic Furniture Company is trying to deter- mine the optimal quantities to make of six possible products: tables and chairs made of oak, cherry, and pine. The products are to be made using the following resources: labor hours and three types of wood. Minimum production requirements are as follows: at least 3 each of oak and cherry tables, at least 10 each of oak and cherry chairs, and at least 5 pine chairs.

The Excel layout and LP Sensitivity Report for Classic Furnitures problem are shown in Screen- shots 4-13A and 4-13B, respectively. The objective function coefficients in the Screenshots refer to unit profit per item. Each of the following questions is independent of the others.

(a) What is the profit represented by the objective function, and what is the production plan?

(b) Which constraints are binding?

(c) What is the range over which the unit profit for oak chairs can change without changing the production plan?

(d) What is the range over which the amount of available oak could range without changing the combination of binding constraints?

(e) Does this Sensitivity Report indicate the presence of multiple optima? How do you know?

(f) After production is over, how many pounds of cherry wood will be left over?

(g) According to this report, how many more chairs were made thanwere required?https://learn.maricopa.edu/files/44778847/download?download_frd=1&verifier=qUIMgC09onqVKctkxKmShLAfDKUrcUT3KO5ZYsUP

4-32Consider the Classic Furniture product mix problem (Problem 4-28). In answering each of the following questions, be as specific as possible. If it is possible to compute a new profit or production plan, do so. (a) A part-time employee who works 20 hours per week decided to quit his job. How would this affect the profit and production plan?

(b) Classic has been approached by the factory next door, CabinetsRUs, which has a shortage of both labor and oak. CabinetsRUs proposes to take one full-time employee (who works 30 hours) plus900 pounds of oak. It has offered $560 as com- pensation. Should Classic make this trade?

(c) Classic is considering adding a new product, a cherry armoire. The armoire would consume 200 pounds of cherry wood and take 16 hours of labor. Cherry wood costs $9 per pound, and labor costs $12 per hour. The armoire would sell for $2,180. Should this product be made?

(d) What would happen to the solution if a con- straint were added to make sure that for every table made, at least two matching chairs were made?

4-28 The Classic Furniture Company is trying to deter- mine the optimal quantities to make of six possible products: tables and chairs made of oak, cherry, and pine. The products are to be made using the following resources: labor hours and three types of wood. Minimum production requirements are as follows: at least 3 each of oak and cherry tables, at least 10 each of oak and cherry chairs, and at least 5 pine chairs. The Excel layout and LP Sensitivity Report for Classic Furniture's problem are shown in Screen- shots 4-13A and 4-13B, respectively. The objective function coefficients in the Screenshots refer to unit profit per item. Each of the following questions is independent of the others. (a) What is the profit represented by the objective function, and what is the production plan? (b) Which constraints are binding? (c) What is the range over which the unit profit for oak chairs can change without changing the production plan? (d) What is the range over which the amount of available oak could range without changing the combination of binding constraints? (e) Does this Sensitivity Report indicate the presence of multiple optima? How do you know? (f) After production is over, how many pounds of cherry wood will be left over? (g) According to this report, how many more chairs were made than were required?https://learn.maricopa.edu/files/44778847/download? download_frd=1&verifier=qUIMgC09onqVKctkxKmShLAfDKUrcUT3KO5ZYsUP 4-32 Consider the Classic Furniture product mix problem (Problem 4-28). In answering each of the following questions, be as specific as possible. If it is possible to compute a new profit or production plan, do so. (a) A part-time employee who works 20 hours per week decided to quit his job. How would this affect the profit and production plan? (b) Classic has been approached by the factory next door, CabinetsRUs, which has a shortage of both labor and oak. CabinetsRUs proposes to take one full-time employee (who works 30 hours) plus900 pounds of oak. It has offered $560 as com- pensation. Should Classic make this trade? (c) Classic is considering adding a new product, a cherry armoire. The armoire would consume 200 pounds of cherry wood and take 16 hours of labor. Cherry wood costs $9 per pound, and labor costs $12 per hour. The armoire would sell for $2,180. Should this product be made? (d) What would happen to the solution if a con- straint were added to make sure that for every table made, at least two matching chairs were made