PLEASE DO Q#4 (a) & (b) & (c) show work ,,,, thank you .

Question number 4

Remember that all explanations must be submitted in one PDF which has the HW cover page as its first page. Make sure you also submit the workbook containing all of your Excel solutions, and make sure that all of your Solver settings are visible when Solver is opened. For all problems make sure to submit both a mathematical formulation and solve the problem in Excel. You may scan handwritten mathematical formulations and graphs, but all other work must be typed. Orange Clockworks, Inc., (OC) manufactures two types of clocks: cuckoo clocks and grandfather clocks. A cuckoo clock sells for $27 and uses 1 lb worth of raw materials. Each cuckoo clock that is manufactured increases OC's variable labor and overhead costs by $14. A grandfather clock sells for $21 and uses 9 lb worth of raw materials. Each grandfather clock built increases OC's variable labor and overhead costs by $10. The manufacture of wooden cuckoo clocks and grandfather clocks requires two types of skilled labor: carpentry and finishing. A cuckoo clock requires 2 hours of finishing labor and 1 hour of carpentry labor. A grandfather clock requires 1 hour of finishing and 1 hour of carpentry labor. Each week, OC has only 100 finishing hours and 80 carpentry hours, and 700 lbs of raw material (costing $10/1b). Demand for grandfather clocks is unlimited, but at most 40 cuckoo clocks are bought each week. OC wants to maximize weekly profit (revenues-costs). Answer the following questions 1. (3 points) Formulate OC's linear program. 2. Graphically deduce: a. (2 points) What the allowable range of change in contribution to profit for each of the clocks that will keep the current solution optimal b. (2 points) What the allowable range of changes in number of finishing hours carpentry hours, and lbs of raw materials that will keep the current basis feasible C. (2 points) The shadow prices of each of the three resources 3. (6 points) Repeat your analysis of problem #1 using MS Excel. 4. How much would OC be willing to pay for: a. (1 point) An additional hour of finishing b. (1 point) An additional hour of carpentry c. (1 point) An additional pound of available raw material