Tutorial Sheet 1: PPC ME 403N Semester 1, 1999-2000

 

  1. Just-in-time has been characterized as a system whose primary goal is to eliminate waste. Discuss how waste can be introduced in
    1. receipt of material into the plant
    2. movement of material through the plant

    How do JIT systems cut down on these forms of waste?

  2. A start-up company, Macrotech, plans to produce a device to translate Morse code to a written message on a home computer and to send written messages in Morse code over the airwaves. The president of the company estimates that it would require a $30,000 initial investment. Each unit costs him $20 to produce and each sells for $85.
    1. How many units must be sold in order for the firm to recover its initial investment?
    2. What is the total revenue at the break even volume?
    3. If the economies of scale kicks in and the cost is estimated to decrease by $2 for every hundred units produced, then what is the break-even point?

     

  3. Based on past experience, a chemicals firm estimates that the cost of new capacities additions obeys the law

f(y) = 0.0205 y.58

where y is measured in tons per year and f(y) in millions of dollars. Demand is growing at the rate of 3,000 tons per year and the accounting department recommends a rate of 12% per year for discounting future costs.
    1. Determine the optimal timing of plant additions and the optimal size of each addition.
    2. What is the cost of each addition?
    3. What is the present value of the cost of the next four additions? Assume an addition has just been made for the purposes of your calculations.

 

  1. A major oil company is considering the optimal timing for the construction of new refineries. From the past experience, each doubling of the size of a refinery at a single location results in an increase in the construction costs of about 68%. Furthermore, a plant of size of 10,000 barrels per day costs $6 million. Assume that the demand for the oil is increasing at a constant rate of two million barrels yearly and the discount rate for future costs is 15%.
    1. Find the values of k and a assuming a relationship of the form f(y) = k ya. Assume that y is in units of barrels per day.
    2. Determine the optimal timing of the plant additions and the optimal size of each plant.
    3. Suppose that the largest single refinery that can be built with current technology is 15,000 barrels per day. Determine the optimal timing of plant additions and the optimal size of each plant in this case.

 
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