Linear programming. Stephen's Furniture Inc. (SFI) employs three carpenters (C1, C2, and C3) and sells two types of furniture (FI and F2). The three carpenters do not work at the same pace and they do not reach the same level of productivity. To maximize his profit, Stephen, the owner, would like to assign the carpenters to the type of furniture for which they are more productive. The accountant of the firm has collected the following information regarding the average time that each carpenter needs to complete a piece of furniture: FI F2 2.00 ci C2 C3 2.50 1:33 hours per unit hours per unit hours per unit 0.80 1.00 0.75 hour per unit hour per unit hour per unit Based on their individual experience, the carpenters carn the following hourly rates: C2 C3 $10/hour $9/hour $11/hour The three carpenters work 40 hours a week. The current market prices for Fl and F2 are, respectively, $55 and $25 for each unit of furniture. In addition to labour, the other variable costs are $10 per unit of Fl and $5 per unit of F2. To satisfy customers' demand. CFI has to produce, weekly, at least 20 units of Fl and 60 units of F2. With the available information, the accountant has formulated the following linear program. This program determines what the production should be to maximize profits, Maximize contribution margin in Scarpenter: C(CIFI. CIF2, C2F1. C2F2, C3F1, C3F2) = 25CIFI + 12C1F2 + 22.5C2F1 + 11C2F2+ 30.37C3F1+11.75C3F2 C(CIFI, CIF2, C2F1, C2F2, C3F1, C3F2)= 25CIFI + 12C1F2 + 22.5C2F1 + 11C2F2+ 30.37C3F1 + 11.75C3F2 Subject to: 2CIFI+ 0.8CIF2 = 20 units of FI CIF2 + C2F2 + C3F2 >= 60 units of F2 CIFI, C2F1, C3F1, CIF2, C2F2, C3F2 >= 0 units of FI & F2 Where: CIFI represents the quantity of type 1 furniture made by carpenter CI C2F1 represents the quantity of type I furniture made by carpenter C2 C3Fl represents the quantity of type I fumiture made by carpenter C3 CIF2 represents the quantity of type 2 furniture made by carpenter CI C2F2 represents the quantity of type 2 furniture made by carpenter C2 C3F2 represents the quantity of type 2 furniture made by carpenter C3 REQUIRED: 1. Formulate and solve the linear programming problem to determine the production mix that will maximize the total contribution margin each week for SFI. 2. Based upon your Solver results, identify how the weekly working time of carpenter C1 will be divided between the two types of furniture. State the impact on SFI's profitability of incrcasing the number of hours carpenter C2 works from 40 to 41 hours a week. Re-run your Solver worksheet. 3. The following information pertains to requirements 4 and 5. 4. 5. With the birth of his second child, carpenter C3 has decided to work only 28 hours a week. Re-run your Solver worksheet again to determine the impact this will have on the weekly total contribution margin of SFI. After a while, carpenter C3 would like to work full-time again (40 hours a week). However, as a condition, he asked the company to pay him a fixed amount of $20,000 per year in addition to his weekly wage of $440 (40 hours per week * $1 l/hour). He argued that his skills allow the company to cam more profit. Explain what the decision of SFI should be on this request. Assumc 50 weeks of work per year