Answer Happy

Please help solve problem 8-28!!
ASSEM- ble. Would this product be economically attractive to manufacture if the sales price were $86? Why or why not? 3-28 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 follow- ing 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 and profit? If it is possible to compute the new profit or production plan, do so. (a) The unit profit for oak tables increases to $83. (b) The unit profit for pine chairs decreases to $13. (c) The unit profit for pine tables increases by $20. (d) The unit profit for cherry tables decreases to $85. (c) The company is required to make at least 20 pine chairs. (f) The company is required to make no more than 55 cherry chairs. 8-30 Consider the Classic Furniture product mix problem (Problem 8-28). For each of the following situations, chairs. SCREENSHOT 8-13A в с D F G H 1 Excel Layout for Classic 1 Classic Furniture Company Furniture Company 2 Oak Oak Cherry Cherry Pine Pine 3 tables chairs tables chairs tables chairs 4 Number of units 3.00 51.67 3.00 85.5642.26 33 08 5 Profit $75 $35 $90 $60 $45 $20 $10,000.00 po 6 Constraints 7 Labor hours 7.5 3.5 9.0 6.0 4.5 2.0 1000.00 <= 1.000 8 Oak (pounds) 200 30 2150.00 <= 2.150 9 Cherry (pounds) 240 36 3800.00 = 3,800 10 Pine (pounds) 180 27 8500.00 8,500 obin 11 Min oak tables 1 3.00 >= 12 Min cherry tables 1 3.00 > den 13 Min oak chairs 1 61.67 >= 10 1 ca 14 Min cherry chairs 10 85.56 >= 15 Min pine chairs 33.08 >= da 16 LHS Sign RHS

248 CHAPTER 8. LINEAR PROGRAMMING SENSITIVITY ANALYSIS SCREENSHOT 8-13B Solver Sensitivity Report for Classic Furniture Company Microsoft Excel 14.0 Sensitivity Report Problems 4-28to32. Classic Furniture Company Variable Cells 0.00 Cell Name $B$4 Number of units Oak tables $C$4 Number of units Oak chairs $D$4 Number of units Cherry tables SE$4 Number of units Cherry chairs $F$4 Number of units Pine tables $G$4 Number of units Pine chairs Final Reduced Objective Allowable Allowable Value Cost Coefficient Increase Decrease 3.00 75.00 0.00 1E+30 51.67 0.00 35.00 1E+30 0.00 0.00 90.00 0.00 1E+30 85.56 0.00 60.00 1E+30 0.00 42.26 0.00 45.00 88.33 0.00 33.08 0.00 20.00 0.00 13.25 3.00 Constraints Cell Name SH$7 Labor hours SH$8 Oak (pounds) SH$9 Cherry (pounds) SH$10 Pine (pounds) SH$11 Min oak tables SH$12 Min cherry tables SH$13 Min oak chairs SH$14 Min cherry chairs $H$15 Min pine chairs Final Shadow Constraint Allowable Allowable Value Price R.H. Side Increase Decrease 1000.00 10.00 1000.00 373.31 37.21 2150.00 0.00 2150.00 318.93 1250.00 3800.00 0.00 3800.00 223.25 2239.78 8500.00 0.00 8500.00 1488.33 5039.50 3.00 0.00 3.00 6.25 2.35 3.00 0.00 3.00 11.33 1.20 51.67 0.00 10.00 41.67 1E+30 85.56 0.00 10.00 75.56 1E+30 33.08 0.00 5.00 28.08 1E+30

DISCUSSION QUESTIONS AND PROBLEMS 247 The Excel layout and LP Sensitivity Report for Classic Furniture's problem are shown in Screen- shots 8-13A and 8-13B, 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 pres- ence 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? Consider the Classic Furniture product mix problem 8.29