Homework #3 Dennis Trotter Jr.

2-11. A large profitable commercial airline company flies 737-type aircraft, each with a maximum seating capacity of 132 passengers. Company literature states that the economic breakeven point with these aircraft is 62 passengers.

a. Draw a conceptual graph to show total revenue and total costs that this company is experiencing.

b. Identify three types of fixed costs that the airline should carefully examine to lower its breakeven point. Explain your reasoning.

c. Identify three types of variable costs that can possibly be reduced to lower the breakeven point. Why did you select these cost items?

 

1) Rent 2)

1) Salaries- must not be too high. 2) Fuel- should find least expensive suppliers. 3) Energy- use efficiently. Because they are three easily controllable items.

2-12 A company produces circuit boards used to update outdated computer equipment. The fixed cost

is $42,000 per month, and the variable cost is $53 per circuit board. The selling price per unit is p = $150 − 0.02D. Maximum output of the plant is 4,000 units per month.

a. Determine optimum demand for this product.

b. What is the maximum profit per month?

c. At what volumes does breakeven occur?

d. What is the company’s range of profitable demand?

a) D* =(a-Cv) / 2b = ($150-53)/ 2*(0.20)=97 / 0.04=2,425 units

b) Profit = Total revenue – Total cost.

P = [a*D^*-b(D^(*^2 )- (Cv*D^*)

= [$150*(2,425) – 0.02 * 〖2425〗^2] – [42,000+53 * (2425)]

= 246137.5 – 170525 = 75612.5

-b〖 *D〗^(2 ) + (a – Cv) * D – Cf = 0

-0.02 *D^2 + (150 – 53) * D – 42,000 = 0

-0.02〖*D〗^2 + 97 * D – 42,000 = 0

-97 ± [〖97〗^2 – 4 * (-0.02) * [(〖-42,000)]〗^.05

D1’ = -97 + 77.8 / -.042 = -37.2588 / -0.042 = 480

D2’ = -97 ± 77.8 / -0.042 = -156.7441 / 0.042 = 4370

2-13 A local defense contractor is considering the production of fireworks as a way to reduce dependence on the military. The variable cost per unit is $40. The fixed cost that can be allocated to the production of fireworks is negligible.

The price charged per unit will be determined by the equation p = $180 − (5)D, where D represents demand in units sold per week.

What is the optimum number of units the defense contractor should produce in order to maximize profit per week?

What is the profit if the optimum number of units are produced?

Cv = $40, Price = 180 – 5*D D = units in demand per week a = 180 b =5

D^* = (a – Cv) / 2*b = (180 – 40) / 2 * 5 = 14 (the maximum produced each week.)

Price = 180 – 5 * 14 = 180 – 70 = $110

Profit = maximum to produce * price – maximum to produce * price =

(14 * $110.0) – (14 * $40.0) = $1540 – $560 = $980

2-14 A large wood products company is negotiating a contract to sell plywood overseas. The fixed cost that can be allocated to the production of plywood is $900,000 per month.

The variable cost per thousand board feet is $131.50. The price charged will be determined by p= $600 − (0.05)D per 1,000 board feet.

For this situation determine the optimal monthly sales volume for this product and calculate the profit (or loss) at the optimal volume.

What is domain of profitable demand during a month?

CF = $900,000, Cv per/1000ft = $131.50, p = $600 – (0.05) * D, a = 600, b = 0.05

D^* = (a – Cv) / 2 * (b) = (600 – $131.50) / (2 * 0.05) = 468.5 / .1 = 4,685

P = [a * D^* – b * (D^(*^2 ))] – CF + [Cv + D^*]

= 600 * (4,685) – 0.05 * $21,949,225 – $900,000 + $4685

= $2,811,000 – $109,7461.25 – $904,816.5 = $808,722.25

(〖9409 – .8* 73,000〗^.5) =

2-15 A company produces and sells a consumer product and is able to control the demand for the product by varying the selling price. The approximate relationship between price and demand is

p = $38 + (2,700 / D) – ( 5,000/D^2), for D > 1,

Where p is the price per unit in dollars and D is the demand per month. The company is seeking to maximize its profit. The fixed cost is $1,000 per month and the variable cost (cv) is $40 per unit.

What is the number of units that should be produced and sold each month to maximize profit?

b. Show that your answer to Part (a) maximizes profit. Cf = 1000, Cv = 40

 

Profit = Tr – Ct

(15x + 14.7x^2)-(12+ 0.3x+0.27x^(2 )) = 0.47x^2 – 14.

dp/dx= 14.7 – (0.47) *(2)x = 0 x = 14.7/0.94 = .638

2-17 The annual fixed costs for a plant are $100,000, and the variable costs are $140,000 at 70% utilization of available capacity, with net sales of $280,000. What is the breakeven point in units of production if the selling price per unit is $40?

Cv = $140,000, Cf = $100,000, net sales = $280,000, unit cost = $40.00.

D = (net sales)/(unit cost) D = $280,000/$40 = 7000 units PD’ = Cf + Cv*D’ D’ = Cf/(P-Cv) = $100,000/($40-$20) = $100,000/$20 = 5000 units

2-19 A cell phone company has a fixed cost of $1,000,000 per month and a variable cost of $20 per month per subscriber. The company charges $29.95 per month to its cell phone customers.

Cf = $100,000 Cv = $20 $29.95 per month for each customer

What is the breakeven point for this company?

D’ breakeven = Cf/(P-Cv) = $100,000/($29.95-$20) = 10050.25126.

b. The company currently has 95,000 subscribers and proposes to raise its monthly fees to $39.95 to cover add-on features such as text messaging, song downloads, game playing, and video watching.

What is the new breakeven point if the variable cost increases to $25 per customer per month?

New D’ breakeven = Cf/(newP-newCv) = $100,000/($39.95-$25) = $100,000/$14.95 = 6688.963

c.