A soccer team’s parent company, Lanternyard Inc., determines the prices for matc

Question

A soccer team’s parent company, Lanternyard Inc., determines the prices for match tickets. Let’s assume that there is only
one type of ticket for matches in their stadium and that the relationship between the demand D (as the number of persons)
and the price for a match ticket (in TL) is described by p = 80 0.001 D+ 100000/D. The company has estimated that it
has a fixed cost of 54,000 TL per match and a variable cost of 27 TL per person. The stadium has a maximum capacity of
33,500 people.
a) What is the profitable range of demand for each match?
b) Find the profit-maximizing level of demand for each match. What is the ticket price at this level of demand? What is
the total profit?
c) How would your answer to parts (a) and (b) change if the stadium had a maximum capacity of 15,000 people?
d) Usng Excel, plot total revenue, total cost and total profit on the same chart. Locate and mark the quanttes asked in
parts (a), (b), and (c) on this chart.
e) Construction/investment mogul Donald McTrump wants to buy this stadium from Lanternyard. Suppose the stadium
hosts about 48 matches per year in their stadium, and that the total profit from each match is as you found in part (b).
Lanteryard asking price is the capitalized worth of the stadium using a MARR = 1.6% per month. Calculate this
price.
f) Perform an Excel analysis of the PW of the stadium versus its “useful life” (with no salvage value). Using the
MARR above, plot the PW of the stadium versus its useful life in months. By trial and error, find the value N of the
useful life where the increase in the PW by adding one more month is less than (i) 1000 TL, (ii) one ticket price, or
(iii) 1 TL. Express your results in years and months for better interpretation.

Explanation / Answer

a) profitable range of demand is when TR>TC

TR = p*D = 80D-0.001D^2+100000

TC = 54000+27D

TR-TC>0 i.e. 53D-0.001D^2+46000>0

Solving for this we get -854<D<53854 but D can be 0 to 33500 So profitable range for D is (0,33500)

b) Profit is maxium when MR=MC

MR = dTR/dD = 80-0.002D

MC = dTC/dD = 27

so D = 26500

p = 80-0.001D+100000/D = 57.27TL

Profit = 53*D-0.001D^2+46000 = 748250TL

c) If maximum capacity is 15000 then answer for a will be (0,15000)

As profit maximum quantity is 26500 but the maximum capacity is 15000 so here the profit maximizing D = 15000

p = 71.67TL

Profit = 616000TL

d)

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