Hello, I am preparing for my exam and this is one of the questions in practice paper. Could you help me with these questions please?
Linear programming basics1) This problem is based on "Giapetto Woodcarving" lab exercise. A toy manufacturerproduces wooden toys of two types. Soldiers sell for $30 and cost $24 to produce, perpiece, while trains sell for $25 and cost $20 to produce, per piece. Making one soldierrequires 0.5 hours of finishing labour and 0.25 hours of carpentry labour. Making onetrain requires 0.25 hours of finishing labour and 0.25 hours of carpentry labour. There are120 hours of finishing labour and 80 hours of carpentry labour available per day. Thedaily demand is 50 soldiers and 200 trains. The company’s objective is to maximizeprofit. A linear programming model has been used to find the optimal number of each toyto make. The screenshot below provides the information about the optimal solution.Questions follow below the screenshot.6Variable Cells7Final Reduced Objective Allowable Allowable8CellNameValue Cost Coefficient Increase Decrease9$C$14 SL4006410SC$15 TR120051IN1112Constraints13Final Shadow Constraint Allowable Allowable14CellNameValuePriceR.H. Side Increase Decrease15$G$14 # of finishing hours used100210052016$G$15 # of carpentry hours used80880205a. Let SL denote the number of soldiers and TR denote the number of trains to make.Complete the problem formulation by specifying the constraints:(10 marks)Objective: maximize 6*SL+5*TRDecision variables: SL, TRConstraints:b. Giapetto can increase the number of labour hours at cost of $4 per hour. Make arecommendation justified by the data from the sensitivity report.(10 marks)c. The production facility has air conditioning unit (AC) but it has not been used. "Touse or not to use: that is the question" has been spinning in Giapetto’s head. Usingthe AC during a day costs $50. However, when it is used, it increases theproductivity of carpentry workers by 10%. On the other hand, it decreases theproductivity of finishing workers by 20% (because colder air slows down drying ofpaint). Formulate an appropriate linear model (the objective, decision variables andconstraints)(10 marks)