3 The cost of operating a large ship (Co) varies as the square of its velocity (v); specifically, Co = knv-, where n is the trip length in miles and k is a constant of proportionality. It is known that at 14 mi/hr, the average cost ofoperation is $135 per mile. Th owner of the ship wants to minimize the cost of operation, but it must be balanced against the cost of the perishable cargo (Cc) which the customer has set at $120 per hour. For a trip lengthof 10 mi, (a) at what velocity should the trip be planned to minimize the total cost (CT), (b) Verify if the answer in (a) minimizes the total cost (c) What is the total cost at the optimum velocity?.Attach FileBrowse Local FilesBrowse Content Collection

Step 1 Given: The cost of operating a large ship (CO) varies as the square of its velocity (v);…

Answered: The cost of operating a large ship (Co)…

Survey Of Economics

10th Edition

ISBN:9781337111522

Author:Tucker, Irvin B.

Publisher:Tucker, Irvin B.

Chapter6: Proudction Costs

Section: Chapter Questions

Problem 8SQP

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= 2. The cost of operating a jet-powered commercial (passenger- carrying) airplane varies as the three-halves (3/2) power of its velocity; specifically, Co kny3/2, where n is the trip length in miles, k is a constant of proportionality, and vis velocity in miles per hour. It is known that at 400 miles per hour, the average cost of operation is $300 per mile. The company that owns the aircraft wants to minimize the cost of operation, but that cost must be balanced against the cost of the passengers' time (CC), which has been set at $300,000 per hour. At what velocity should the trip be planned to minimize the total cost, which is the sum of the cost of operating the airplane and the cost of passengers' time?
The variation of the total production cost with the production rate for a process is defined as follows. ALL = 2 000 000 + 4q + 2.5 q1.1 (ECU / year) q [=] kg / year a) Plot the change of total production cost according to the production speed. b) Find the annual fixed and variable costs for the case where the production rate is 2 000 000 kg / year. c) Find the average and interface costs for the same production capacity. d) If the market selling price of the product is 20 ECU/ unit, what should be the minimum production rate in order not to damage the organization?
If company A manufactures t-shirts and sells them to retailers for US$9.80 each. It has fixed costs of $2625 related to the production of the t-shirts, and the production cost per unit is US$2.30. Company B also manufactures t-shirts and selll them directly to consumers.The demand for its product is p = 15 −x 125, its production cost per unit is US$5.00 and its fixed cost are the same as for company A . (i) Derive the total revenue function, R(x) for company A. (ii) Derive the total cost function, C(x) for company A. (iii) Derive the profit function, Π(x) for company A. (iv) Using a spreadsheet, create a table for showing x, R(x)?, C(x) for company A in the domain x = 50, 100, 150, 200, 250, 300, 350, 400, 450.(v) Graph the functions from (d) above on the same axes. (vi) From your graph, determine the break-even level of output for company A. (vii) Derive the total revenue function, R(x) for company B. (viii) Derive the profit…
If company A manufactures t-shirts and sells them to retailers for US$9.80 each.It has fixed costs of $2625 related to the production of the t-shirts, and the production cost perunit is US$2.30. Company B also manufactures t-shirts and sell them directly to consumers.The demand for its product is p = 15 −x 125, its production cost per unit is US$5.00and its fixed cost are the same as for company A.(i) Derive the total revenue function, R(x) for company A.(ii) Derive the total cost function, C(x) for company A.(iii) Derive the profit function, Π(x) for company A.(iv) Using a spreadsheet, create a table for showing x, R(x)?, C(x) for company Ain the domain x = 50, 100, 150, 200, 250, 300, 350, 400, 450.(v) Graph the functions from (d) above on the same axes.(vi) From your graph, determine the break-even level of output for company A.(vii) Derive the total revenue function, R(x) for company B.(viii) Derive the profit function,…
If company A manufactures t-shirts and sells them to retailers for US$9.80 each.It has fixed costs of $2625 related to the production of the t-shirts, and the production cost perunit is US$2.30. Company B also manufactures t-shirts and selll them directly to consumers.The demand for its product is p = 15 −x125 , its production cost per unit is US$5.00and its fixed cost are the same as for company A . (vii) Derive the total revenue function,R(x) for company B.(viii) Derive the profit function,Π(x) for company B.(ix) How many t-shirts must company B sell to in order to break-even.(x) How many t-shirts must company B sell to maximise its profit
Cost, revenue, and profit are in dollars and x is the number of units. A firm knows that its marginal cost for a product is МС- 4x+ 25, that its marginal revenue is MR%3D 75 - 6х, and that the cost of production of 60 units is $8,880. (a) Find the optimal level of production. units (b) Find the profit function. P(x) = (c) Find the profit or loss at the optimal level.
Disc Buddy, Inc. produces flash drives. The selling price is $8 per drive. The variable cost of production is $2.40 per unit and the fixed cost per month is $3,600. Calculate the contribution margin associated with each flash In August, the company sold 200 more flash drives than What is the expected effect on profit of selling the additional drives?
A jeweler is considering producing a limited edition diamond bracelet, and she is trying to decide how many bracelets to produce. The table gives her estimated total cost for various production levels as well as the price she would charge for each bracelet. Number of bracelets 100 200 300 400 500 600 Total cost (thousands) Price per bracelet $215 $7900 $420 $7400 $625 $5900 $820 $5000 $1015 $4200 $1205 $3600 (a) of the production levels listed in the table, which gives the highest profit? (b) Estimate the marginal cost and marginal revenue when 400 bracelets are made. marginal cost $ marginal revenue $
A manufacturer sells a product at $9.45 per unit, selling all produced. The fixed cost is $2325 and the variable cost is $8.20 per unit. At what level of production will there be a profit of $5000? At what level of production will there be a loss of $1550? At what level of production will the break-even point occur? There will be a profit of $5000 when the production level is units.
Your friend Claire has been designing her own hoodies and giving them as gifts to friends and family. She has decided to sell them online soon by using a 3rd party website with a service surcharge based on her pricing. Using the information below, what is the relationship between Claire's selling price per hoodie and profit margin? (Please plot a graph dipcting the relationship) Costs ($) Base Hoodie Cost $30 Craft Supplies to design $10 Selling Website Service Charge 5%
Intelligent Inc. specializes in the manufacture ofcomponents for personal computers. Managementhas determined that the daily cumulative cost of producing these components (in dollars) is given by:C(x) = 0.0001x3 - 0.08x2 + 40x + 5000where x is the number of components produced.(a) What is the actual cost incurred for manufacturing the 301st component?(b) What is the marginal cost of the 200th component? What can you say about the marginal costas a function of x (increasing or decreasing)?(c) What is the average unit cost if you produce just300 units?
A company has established that the relationship between the sales price for one of its products and the quantity sold per month is approximately p = 78 – 0.11D units. The fixed cost is $800 per month and the variable cost $32 per unit produced. What number of units, D*,should be produced per month and sold to maximize the profit per month related to the product? Round your answer to 2 decimal places.

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