For a particular flight from Dulles to SF, an airline uses wide-body jets with a capacity of 440 passengers. It costs the airline $4,000 plus $70 per passenger to operate each flight. Through experience the airline has discovered that if a ticket price is $T, then they can expect (440−0.64T) passengers to book the flight. Determine the ticket price, T, that will maximize the airline's profit.
Answers
Answer:
$378.75
Explanation:
Data provided:
Capacity = 440 passengers
Operating cost = $4,000 + $70(Number of passengers)
Expected number of passengers = 440 - 0.64T
Ticket price = T
Total operational cost = $4000 + $70( 440-0.64T )
Total operational cost = $34,800 - 44.8T
Thus,
Total revenue = Number of passengers × Ticket price
= (440 - 0.64T)T
= 440T - 0.64T²
also,
Total profit ,P(T) = Total revenue - Total operational cost
P(T) = ( 440T - 0.64T²) - (34,800 - 44.8T)
P(T) = - 0.64T² - 34,800 + 484.8T
Now,
Differentiating with respect to ticket price T
P'(T) = -0.64(2)T - 0 + 484.8(1)
or
P'(T) = - 1.28T + 484.8 ..............(1)
For point of maxima or minima
P'(T) = 0
or
- 1.28T + 484.8 = 0
or
1.28T = 484.8
or
T = $378.75
now,
again differentiating (1) to check for maxima or minima
P''(T)= -1.26(1) + 0
P''(T) = -1.26
Since,
P"(T) < 0
Hence,
T = $378.75 will maximise the profit
Final answer:
The airline's profit can be maximized with a ticket price of approximately $289.84 as calculated from the provided mathematical model. However, real-world variables may affect actual optimal pricing.
Explanation:
In this case, the airline's profit function (revenue minus costs) can be written as: P(T) = T*(440 - 0.64T) - (4000 + 70*(440 - 0.64T)). To maximize profit, you would take the derivative of P(T) with respect to T, resulting in the following polynomial: P'(T) = 440 - 1.28T - 70. Setting this derivative equal to zero and solving for T yields a ticket price of approximately $289.84.
Another way to check this solution would be to create a graph of the function P(T) and visually identify the maximum point. Mind you, this method requires precision and may not generate the accurate result as the calculus method.
It's important to keep in mind that this is a simplified model and doesn't account for other factors which can affect ticket pricing in the real world, such as competition, fuel prices, and demand for specific flights. That being said, this exercise highlights how mathematical models can be used in economics and business to optimize profit by adjusting pricing strategies.
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Related Questions
1.Calculate the present value (PV ) of a cash inflow of $500 in one year, and a cash inflow of $1,000 in 5 years, assuming a discount rate of 15%.
On December 31, it was estimated that goodwill of $51,500 was impaired. In addition, a patent with an estimated useful economic life of 12 years was acquired for $115,200 on April 1.a. Journalize the adjusting entry on December 31 for the impaired goodwill b. Journalize the adjusting entry on December 31 for the amortization of the paten
Roenfeld Corp believes the following probability distribution exists for its stock. What is the coefficient of variation on the company's stock? Probability Stock's State of of State Expected the Economy Occurring Return Boom 0.45 25% Normal 0.5 15% Recession 0.05 5% 0.2839 0.3069 0.3299 0.3547 0.3813
Fortune Company's direct materials budget shows the following cost of materials to be purchased for the coming three months: January February March Material purchases $ 13,180 $ 15,290 $ 12,110 Payments for purchases are expected to be made 50% in the month of purchase and 50% in the month following purchase. The December Accounts Payable balance is $7,900. The expected January 31 Accounts Payable balance is:______________.
Answers
Answer:
5
Explanation:
15 - 10 = 5
Answers
Answer:
6.47%
Explanation:
The computation of effective annual yield is shown below:-
Annual YTM = 6.37%
Semiannual YTM = 6.37% ÷ 2
= 3.185%
Effective Annual Yield = (1 + Semiannual YTM)^2 - 1
= (1 + 0.03185)^2 - 1
= 1.03185^2 - 1
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or
= 6.47%
Hence, the effective annual yield is 6.47% i.e come after applying the above formula
B. The tuition you pay during your first year of college.
C. The social security check your grandmother receives.
D. A new purchase of 50,000 shares of Time/Warner stock.
E. A new pair of tennis shoes made in China and purchased by an American shoe store.
Answers
Answer:
A. A new airplane purchased by United Parcel Service.
- Investment (in fixed assets), GDP grows
B. The tuition you pay during your first year of college.
- Consumption (of services), GDP grows
C. The social security check your grandmother receives.
- Not included in GDP, social security checks are considered transfer payments.
D. A new purchase of 50,000 shares of Time/Warner stock.
- Not included in GDP, only IPOs are included in GDP
E. A new pair of tennis shoes made in China and purchased by an American shoe store.
- Import, GDP decreases since net exports decrease
Explanation:
Answers
Answer:
The cost of land to be reported is $174,750
Explanation:
The cost of land reported in the Balance sheet does not only include the price paid to acquire the Land but also include any costs/revenue received in the processes, activities needed to bring the land to the stage in which it may be ready for usage.
Thus, besides the price paid which is $140,000 ( $90,000 cash and $50,000 short-term note), we have to add-up all the relevant costs including Legal fees, delinquent taxes, Removal of old building expenses and deduct the material salvaged gain from demolition of old building. The construction cost of new warehouse is irrelevant here as without this cost, the Land is already in a ready-to-use stage ( i.e: for building new property in the Land)
So, the amount of Cost of Land to be reported is : 140K + 1,75K + 25K + 9K - 1K = $174,750
Final answer:
The cost of the land to be reported on the balance sheet is $174,750.
Explanation:
To determine the cost of the land to be reported on the balance sheet, we need to add up all the costs associated with acquiring and preparing the land. In this case, the costs include the cash payment of $90,000, the short-term note of $50,000, legal fees of $1,750, delinquent taxes of $25,000, and fees paid to remove the old building of $9,000. We then subtract the salvage value of the materials sold, which is $1,000. So the total cost of the land is:
Total cost of land = Cash payment + Short-term note + Legal fees + Delinquent taxes + Fees to remove old building - Salvage value of materials
= $90,000 + $50,000 + $1,750 + $25,000 + $9,000 - $1,000 = $174,750
Therefore, the cost of the land to be reported on the balance sheet is $174,750.
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The president of the United States argues that the United States should threaten to impose a tariff on Chinese steel rods in order to induce the Chinese to remove its tariff on American cars.
Which of the following justifications is the pundit using to argue for the trade restriction on steel rods?
a. National-security argument
b. Infant-industry argument
c. Jobs argument
d. Using-protection-as-a-bargaining-chip argument
e. Unfair-competition argument
Answers
Jobs argument justifications is the pundit using to argue for the trade restriction on steel rods
Explanation:
A main argument often put forward to curb trade would be that trade decreases the amount of jobs domestically available.
The point about maintaining jobs is often put forward by employers to protect union jobs. Nevertheless, unions are undermining the market by prohibiting businesses from receiving their products at lower prices, causing them to increase prices. Moreover, businesses are often discouraged from using automation or robotics to retain jobs, which is ironic because automation and robotics improve the productivity of workers, thereby encouraging companies to pay employee salaries and benefits.
Answers
Answer:
Incremental cost of buying the component = $69,500
Therefore the component shall be make in the company and shall not be bought from outside.
Explanation:
Provided the cost in case of manufacturing
65,000 units
Variable Cost = $1.9565,000 = $126,750
Fixed Cost = $75,000
Total cost of making the product = $126,750 + $75,000 = $201,750
Total cost in case of buying the product
Price to be paid = $3.25 65,000 = $211,250
Also the fixed cost of $60,000 will be incurred in any manner and is not avoidable.
In that case total cost of buying the product = $211,250 + $60,000 = $271,250
Incremental cost of buying the component = $271,250 - $201,750 = $69,500
Therefore the component shall be make in the company and shall not be bought from outside.
Final answer:
If Gilberto Company purchases the part externally, it will incur an extra cost of $12,750. Therefore, it is more cost-effective for the company to continue manufacturing the part in-house.
Explanation:
The first step is to calculate the total cost of producing 65,000 units in-house and the total cost of buying 65,000 units externally.
For in-house production: The cost is the sum of variable costs, fixed costs, and allocated costs, yielding: (65,000 units * $1.95/unit) + $75,000 + $62,000 = $198,500
For external purchasing: the total cost is simply 65,000 units * $3.25/unit = $211,250.
We subtract the in-house cost from the external purchasing cost to obtain the incremental cost: $211,250 - $198,500 = $12,750. Therefore, it costs an incremental $12,750 to buy 65,000 units externally compared to making them in-house. Considering the cost-effectiveness, Gilberto Company should continue to manufacture the parts in-house rather than buying them from the external supplier.
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