Assistance with a quiz

I have a quiz in Micro (below) can you assist by Saturday? An insulation plant makes three types of insulation (types B, R and X). Each is produced on the same machine which can produce any mix of output so long as the daily total weight is no more than 70 tons. The insulation is shipped in trucks from the company loading dock which can process a maximum of 30 trucks per day. The trucks can carry any mix of types B, R and X insulation. A truckload of type B, R and X insulation weighs 1.4 tons, 2.8 tons and 1.9 tons respectively. The insulation carries a flame retarding spray that is currently in short supply and only 75 cans of the spray are available daily. A truckload of type B insulation requires 3 cans of the spray, type R requires 1 can per truckload and type X requires 2 cans per truckload. Demand for each type of insulation is very strong and the company anticipates no problem selling the plant’s entire output. The contribution margin for type B insulation is $1,425 per truckload, whereas for types R and X insulation, the contributions are $1,800 and $1237.50 per truckload, respectively. The company is interested in determining how much of each insulation type it should produce. A. Develop the linear programming formulation for the above problem. Make sure you define and label your variables, clearly show the objective function and the relevant constraints in their algebraic form. (30 points) B. Translate the above into a Solver formulation of the linear programming problem and solve it. Attach the spreadsheets showing the formulations, the answer report, sensitivity report and limits report. (40 points) C. Describe the optimal production policy: (40 points) 1. How much of each insulation type (B, R and X) should be produced? 2. Identify and the slack and binding constraints at the optimal production level. 3. What is the total contribution at this production level? D. Use the appropriate reports from the Solver output to answer the following questions. (60 points) 1. What would you be willing to pay for (i) an extra unit of machine time, (ii) an extra unit of loading dock capacity and (iii) an extra canister of flame retarding spray? Explain your reasoning. 2. Suppose the machine needs downtime for preventive maintenance that will reduce its daily total output by 10%. How will this affect your answers to Part C? Explain your reasoning. 3. Is a likely improvement in the availability of flame retarding spray (10 extra cans per day) affect your answer to Part C? Explain your reasoning. E. The price of type X insulation has increased by $250 per truckload due to demand stemming from a new application. How will this change your answer to Part C? Explain your answer. (30 points) Q2. (200 points) Chuck Raverty is the managing partner of a small boutique consulting firm in which he has four senior partners available to work on four current projects for during the coming month. Chuck has assessed the fit between the skill levels of his colleagues relative to each of the four projects and has rated them on a 0-100 scale. Not surprisingly, the ratings are all fairly high, but there still are significant differences in the quality of fit. The following is a table of the ratings that he has developed: Partner Project 1 2 3 4 Alan 90 80 25 50 Charlie 60 70 50 65 David 70 40 80 85 Robert 65 55 60 75 Time 140 100 170 70 The last row of the table shows Chuck’s assessment of the time that it will take to complete each of the four projects. A. Assume that each partner will be assigned only to one project. What is the assessment of partners to projects that will maximize the sum of the assigned quality scores? Develop and write down the formal mathematical statement of the problem. (40 points). B. Set up the Solver spreadsheet model for the problem above. Use Solver to solve the problem, obtain the relevant reports and interpret your answer. (40 points). C. Support that each of the four partners has only 160 hours of time available in the coming month. Assume that more than one partner can work on a project. What assignment schedule will maximize the sum of the assigned quality scores? As in Part A, develop and write down the formal mathematical statement of the problem. (50 points) D. Set up the Solver spreadsheet model for the problem in Part C. Use Solver to solve the problem in Part C, obtain the relevant reports and interpret your answer. (50 points) E. Suppose that Chuck does not want to assign multiple partners to the same project but is willing to provide an incentive for each partner to work the overtime needed. Based on the solutions obtained in Parts B and D, develop a comparison of the quality levels of the projects that are delivered. Assuming that a point of increased project quality is worth $1,000 to him, what should he be willing to pay for the quality maximizing solution? (200 points).

   Related Questions in Microeconomics

  • Q : Functions of Profits and Losses The

    The functions of profits into a market economy do NOT comprise: (1) stimulation for firms to be innovative and efficient. (2) compensating savers for delays of consumption. (3) signaling changing business conditions. (4) inducing mimi

  • Q : Moral Hazard-Equilibrium wage If

    If workers know that they are guaranteed a particular weekly wage and can simply find another job at this equilibrium wage, then some workers tend to loaf or shirk. This is an illustration of: (i) Adverse selection. (ii) Moral hazard. (iii) Demand and supply. (iv) Ine

  • Q : Nondiscriminating monopolists in short

    Within short run equilibrium, there nondiscriminating monopolists will: (w) charge prices greater than their marginal costs. (x) produce outputs which maximize social welfare. (y) produce where their total revenues are maximized. (z)

  • Q : Market initially at price and quantity

    This market for peanuts is primarily into equilibrium at price: (w) P0 and quantity Q0 (x) P1 and quantity Q0 (y) P2 and quantity Q2 (z) P1 and quantity Q1

  • Q : Monopolies over brand name products of

    Several firms have monopolies over brand name products, although face competition from: (w) international cartels. (x) oligopolistic rivals. (y) producers of close substitutes for their products. (z) intra-firm rivalry.

    Q : Problem on zero bond price You are

    You are provided a bond which will pay no interest however will return the par value of $1,000 20 years from now. When your needed return for this bond is 7.35%, what are you willing to reimburse or pay?

  • Q : Problem regarding to price ceilings and

    Persistent shortages of a good are mostly all the time attributable to: (w) legal ceiling prices that are set below equilibrium. (x) recessions that yield high unemployment rates. (y) price gouging by firms with monopoly power. (z) legal price floors

  • Q : Comparable the changes in TC and TVC

    Tell me the answer of this question. In comparing the changes in TC and TVC associated with an additional unit of output, we discover that: A) the change in TVC is equal to MC, while the change in TC is equal to TFC. B) the change in TC exceeds the change in TVC. C) t

  • Q : All possible prices exceeding in

    Participants in this market would experience a surplus in this market for teleporter buttons: (1) at all possible price per button exceeding P2. (2) equal to distance cd when the price per button equals P1. (3) when this market was primarily in e

  • Q : Tax onto the mathematically impaired By

    By the opinion of public finance economists and financial analysts that the label “a tax onto the mathematically impaired” is most likely most applicable to: (1) land taxes. (2) income taxes. (3) inheritance taxes. (4) purchases of lottery

©TutorsGlobe All rights reserved 2022-2023.