ETW 1010
Assignment 3: Answer All Questions
Question 1 [25 points]:
An oil refinery uses two types of crude oil: light crude, which costs $35 a barrel, and heavy crude, which costs $30 a barrel. The refinery can produce three different types of fuel from either type of crude oil, with varying levels of efficiency. For each barrel of crude oil, the refinery can produce the following litres of fuel:
Gasoline Heating fuel Jet Fuel
Light Crude 0.6 0.2 0.5
Heavy Crude 0.3 0.5 0.2
The refinery has a current contract to supply 900,000 litres of gasoline, 800,000 litres of heating fuel, and 500,000 litres of jet fuel. The refinery needs to find the amounts of light and heavy crude to purchase to meet these current supply requirements at a minimum cost.
1.Formulate the mathematical model for this problem. [10 pts]
2.Solve this problem in Excel assuming that the company can purchase partial barrels of crude. [3 pts]
3.State the optimal solution and the total cost at the optimal solution. [2 pts]
4.Assuming the price of light crude stays the same, at what price of heavy crude will the oil refinery shift all production to be carried out using heavy crude? [10 pts] [Hint: it will help to draw the feasible region diagram]
Question 2 [25 points]:
“The Table Company” manufactures two types of tables – oak dining tables and fake oak laminate dining tables, referred to as “foak” tables. The company must fulfil an order for 30,000 oak tables and 15,000 foak tables. The company has a choice of manufacturing the tables in house or outsourcing their production to a third party manufacturer. It costs the company $75 to produce one oak table and $67 to produce one foak table. It costs $85 and $70 to outsource the oak and foak tables, respectively.
The time at each stage of production for every table produced in house is given in the following table:
Hours required per table
Department Oak table Laminate table
Cutting raw timber and sanding
Covering with overlay/staining
Packaging 0.6
0.5
0.2 0.4
0.5
0.1
Available hours are limited to 10,000, 15,000 and 5,000 for the cutting, covering and packing departments, respectively.
1.Develop a mathematical model for this problem (the company is interested in minimizing the overall cost of production). [8 points]
2.Solve this problem using Excel. [5 points]
3. How many oak and foak dining tables will the company manufacture in house and how many will it outsource? [2 point]
4. What is the minimum cost at the optimal solution? [2 point]
5. At what cost for producing oak tables in house would the company be indifferent between producing oak tables and outsourcing them? [3 points]
5.If the cost to make laminate tables in house increased to $90 p
Question 3 [25 points]:
The investment bank “ET720 Investments” is deciding on which of four bonds to invest in over the next two years. The investment details for the bonds are given in the table below:
Investment Requirements ($)
Year 1 Year 2
Bond A
Bond B
Bond C
Bond D 32,000
15,000
8000
10,000 17,000
21,000
9500
7000
The net worth of these four bonds at the end of the two years is $65,000, $60,000, $25,500, and $18,000, respectively. The funds available for investment in year 1 and year 2 are $35,000 and $62,000, respectively.
1.Develop and solve a binary integer programming model for maximizing the net worth of the investment, assuming ET720 can only invest in one bond. Be sure to build a clear mathematical model and then implement this model in excel. [10 pts]
2.Suppose now that the firm must invest in Bond B, and that they must also invest in one of the remaining three bonds (bringing the total number of investments to two). Modify your formulation from part 1 to reflect this new situation. [10 pts]
3. Compare your answer to 1 and 2. Which solution yields a higher total net worth? [5 pts]
Question 4 [35 marks]
Irene has always designed her own birthday cards. In fact she enjoys designing cards so much that she is considering starting up a card design business. She will work from home, and market her cards by means of hand-delivered pamphlets. She employs a delivery person to deliver these pamphlets at 5 cents per pamphlet. Printing these pamphlets costs a fixed sum of $2,500, plus an extra 12 cents for each pamphlet printed. Cards come in bundles of 20 for a price of $80, of which $50 covers Irene’s variable production costs. Most customers only purchase one bundle of 20 cards at a time.
(a)Suppose Irene decides to print and deliver 2000 pamphlets. Construct a concept diagram and a mathematical model. Consider a trial response rate of 10%.
(b)Construct a spreadsheet model and determine the estimated profit based on this trial response rate. Should Irene start up her business?
(c)Determine the sensitivity of profit to the response rates using data table. Use response rates of 1% to 15%
(d)Graph the response rate against the resulting profit figures. Based on the chart and Part (d), what is the estimated minimum response rate required for Irene’s business to break even? Using Goal Seek determine a more precise answer.
(e)Irene is willing to continue delivering pamphlets even if the response rate is 3%. Explain her reasoning behind this.
(f)How do your results change if, instead of a per-pamphlet rate, the delivery person is paid a one-off sum of $50 plus a commission of $1 per bundle of cards sold? Identify other factors that would influence your results.
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