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The equations modeling supply and demand for flights on Route X per year is given byp 1500 10 q = a2 p 0.
The equations modeling supply and demand for flights on Route X per year is given byp 1500 10 q = − a2 p 0.0001q 2 q 200 = + + bWhere p is market price in dollars and q is the number of passenger flights, in thousands per year.The airline estimates that over the last year on this route aviation fuel costs have increasedby approximately $80 per passenger. To compensate for this and future increases the airlineis considering a fuel surcharge of $100 per passenger flight on this route.As a consultant you have been asked to explore and report on the consequences of thisproposed surcharge, in particular the effect on demand. You are required to provide, andjustify a recommendation, to the airline on whether to introduce the proposed fuelsurcharge or not.ASSIGNMENT 1B TASKSChoose CoefficientsUse the Excel random function =Rand() or the RANDOM key on your calculator to obtaintwo random numbers between 0.1 and 0.9 (inclusive) rounded to 1 decimal place.Replace coefficients a and b with these random numbers and enter them of page 2 ofAssignment 1B coversheets.Mathematical Working (16 marks)The following mathematical tasks should appear as an appendix to your written answerbelow. This should include all necessary steps and appropriate Excel, or equivalent, output.The appendix should be in one of the following formats:• Word with Excel output embedded (use Paste Special --> Excel Object)• Use the Microsoft equation editor or MathType for writing equations.For ease of marking please your appendix should be copied to the end of your worddocument. MAT10706 Session 2 2014 SCU college Assignment 1, page 6Tasks1. Algebraically find the equilibrium price and quantity, without the proposed surcharge.2. Update the demand equation to include the proposed surcharge.3. Algebraically find the updated equilibrium price (without surcharge) and quantity.4. Use Excel to graph on the same set of axes, the original supply and demand equationsand the updated demand equation with the proposed surcharge.5. Use your results to complete the following summary tableBeforeSurchargeAfterSurchargeDifference Change %Equilibrium QuantityEquilibrium Price: Consumer PaysEquilibrium Price: Airline receives(without any fuel surcharge)Revenue airline receives from route,(without any surcharge)Revenue airline receives from fuelsurcharge--- --- ---Hints:• Use the quadratic formula in Tasks (1) and (3)• In Tasks 2 and 3 p is the market price without the proposed surcharge, the consumerwill pay this plus the surcharge.• Check that the equilibrium quantities obtained are correct, that is, Supply equalsDemand.• Check that the equilibrium quantities obtained in Tasks 1 and 3 are consistent with thegraph.Written Answer (7 marks)Maximum of 1 page and 250 words.Communicate the results of your calculations briefly as two or three paragraphs to beincluded in a larger report.You need to:• Introduce the current situation without the proposed surcharge.• Present the results of your calculations in an understandable and non-mathematicalway. Without unnecessary mathematical jargon and equations
