# 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.

\$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

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

The Kilp Sisters Trust is required to distribute \$60,000 annually equally to its two income beneficiaries, Clare and Renee. If trust income is not sufficient to pay these amounts, the trustee can invade corpus to the extent necessary. During the current year, the trust generates only taxable interest income and records DNI of \$160,000; the trustee distributes \$30,000 to Clare and \$150,000 to Renee. a. How much of the \$150,000 distributed to Renee is included in her gross income? \$.
b. How much of the \$30,000 distributed to Clare is included in her gross income? \$ is included in her gross income.
c. The distributions which are composed of trust accounting income that is required to be distributed currently come under .

a)

Results for Renee are as follows:

After the first tier distributions (\$60000/2 = \$30000 to each income beneficiaries) are accounted for, \$100000 DNI remains to be assigned to the beneficiaries on the second tier (\$160000 DNI - \$60000 DNI used for first tier distribution).

portfolio income

First tier             \$30,000.00                       \$30,000.00

Second tier     \$1,20,000.00                        \$ 1,00,000.00

Total            \$1,50,000.00                           \$ 1,30,000.00

b)

Results for Clare are as follows:

portfolio income

First tier                \$30,000.00                         \$ 30,000.00

Second tier            \$ -                                              \$ -

Total                 \$30,000.00                           \$ 30,000.00

c)

The distributions which are composed of trust accounting income that is required to be distributed currently come under First Tier Distribution.

Hiring managers should automatically preclude a candidate with a disability if they appear to be unable to do the job.True or false?

True

Explanation:

I believe it's true. If we have a job opening for sales personnel and candidate is physically unable to walk or drive, then yes we can exclude that candidate. But once hiring manager is sure of the fact that disability will render that candidate unable to work then manager can preclude that candidate.

Arthur Corporation has a margin of safety percentage of 25% based on its actual sales. The break-even point is \$290,400 and the variable expenses are 45% of sales. Given this information, the actual profit is:(Do not round your intermediate calculations.)

\$53,240

Explanation:

We know that,

Break even point = Fixed cost ÷ contribution margin ratio

\$290,400 = Fixed cost ÷ 55%

So, the fixed cost = \$290,400 × 55% = \$159,720

As the variable expense is 45% and we assume the sales is 100%, so the contribution ratio would be 100% - 45% = 55%

Now the margin of safety equal to

= (Expected sales - break even sales) ÷ (expected sales) × 100

25% = (Expected sales - \$290,400) ÷ (expected sales) × 100

25% Sales = (Expected sales - \$290,400)

So, the expected sales would be

= \$290,400 ÷ 75%

= \$387,200

Now the actual profit equals to

= Sales - variable expenses - fixed cost

= \$387,200 - \$174,240 - \$159,720

= \$53,240

The variable expense is computed below:

= \$387,200 × 45%

= \$174,240

Crocetti Corporation makes one product and has provided the following information to help prepare the master budget for the next four months of operations: Budgeted selling price per unit \$ 121 Budgeted unit sales (all on credit): January 7,000 February 7,500 March 11,900 April 14,900 Credit sales are collected: 40% in the month of the sale 60% in the following month The budgeted accounts receivable balance at the end of February is closest to:

The budgeted accounts receivable balance at the end of February is closest to: \$4,500.

Explanation:

Prepare a Accounts Receivable Budget for January and February

January           February

Balance b/d                                \$0                \$4,200

Credit Sales                           \$7,000             \$7,500

Balance c/d                           \$4,200             \$4,500

Conclusion:

Therefore, the budgeted accounts receivable balance at the end of February is closest to: \$4,500

Novak Company acquired a plant asset at the beginning of Year 1. The asset has an estimated service life of 5 years. An employee has prepared depreciation schedules for this asset using three different methods to compare the results of using one method with the results of using other methods. You are to assume that the following schedules have been correctly prepared for this asset using (1) the straight-line method, (2) the sum-of-the-years'-digits method, and (3) the double-declining-balance method.Year Straight-Line Sum-of-the-Years'-Digits Double-Declining-Balance
1 \$15,750 \$26,250 \$35,000
2 15,750 21,000 21,000
3 15,750 15,750 12,600
4 15,750 10,500 7,560
5 15,750 5,250 2,590
Total \$78,750 \$78,750 \$78,750

Required:
a. What is the cost of the asset being depreciated?
b. What amount, if any, was used in the depreciation calculations for the salvage value for this asset?
c. Which method will produce the highest charge to income in Year 1?
d. Which method will produce the highest charge to income in Year 4?
e. Which method will produce the highest book value for the asset at the end of Year 3?
f. If the asset is sold at the end of Year 3, which method would yield the highest gain (or lowest loss) on disposal of the asset?

a. What is the cost of the asset being depreciated?

the cost of the asset = \$35,000 / 0.4 = \$87,500

b. What amount, if any, was used in the depreciation calculations for the salvage value for this asset?

salvage value = \$87,500 - (5 x \$15,750) = \$8,750

c. Which method will produce the highest charge to income in Year 1?

double declining results in the highest depreciation expense

d. Which method will produce the highest charge to income in Year 4?

straight line results in the highest depreciation expense

e. Which method will produce the highest book value for the asset at the end of Year 3?

straight line, book value = \$87,500 - (3 x \$15,750) = \$40,250

f. If the asset is sold at the end of Year 3, which method would yield the highest gain (or lowest loss) on disposal of the asset?

double declining balance, since the carrying value is lowest = \$87,500 - \$35,000 - \$21,000 - \$12,600 = \$18,900

e.g. if the assets is sold at \$30,000, the gain = \$11,100

under straight line method a \$30,000 resale price would result in a loss(= \$30,000 - \$40,250 = -\$10,250), while sum of years' digit would result in a gain = \$30,000 - (\$87,500 - \$26,250 - \$21,000 - \$15,750) = \$5,500

The best cost system to use for a company producing a continuous stream of similar items would be a: Group of answer choices Production costing system. Job order system. No cost system is required when jobs are similar. Process costing system.

The Best Cost System is the "Process Costing System"

Explanation:

A Process Costing System amasses costs when an enormous number of indistinguishable units are being created. Right now, is generally proficient to collect expenses at a total level for an enormous group of items and afterward dispense them to the individual units delivered. The supposition that will be that the expense of every unit is equivalent to that of some other unit, so there is no compelling reason to follow data at an individual unit level. The great case of a procedure costing condition is an oil treatment facility, where it is difficult to follow the expense of a particular unit of oil as it travels through the processing plant.

Explanation: A process costing system used in the manufacturing industry that accumulates the costs of producing a continuous stream of similar items.

It is calculated thus:

Cost per unit = cost of unit/ expected output in unit.

Using process costing method is very efficient to accumulate costs at an aggregate level for a large batch of products and then allocate the cost to the individual units produced.

There are three types of process costing and they are:

1. Weighted Average Cost

2. FIFO - First In First Out

3. Standard Cost