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Problem 11

Define learning curve. Outline two models that can be used when incorporating learning into the estimation of cost functions.

Expert verified

A learning curve is a graphical representation of the relationship between the cumulative output of a process and the time or effort required for each additional unit, showing how the unit cost decreases as cumulative production quantity increases due to increased experience and efficiency. Two models that can be used when incorporating learning into the estimation of cost functions are Wright's Law and DeJong's Progressive Learning Model. Wright's Law states that the cost of producing the Nth unit decreases by a constant percentage known as the learning rate when cumulative production doubles, and is represented by the equation:
C(N) = C1 * N**(-b)
DeJong's Progressive Learning Model suggests that learning follows a gradual approach, where productivity improves as the learning rate increases over time, and is represented by the equation:
C(N) = C1 * N**(a - bn)
Both these models offer different approaches to incorporating learning effects in cost estimation depending on the specific circumstances and the nature of learning in a given organization or workforce.

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Chapter 10

A firm uses simple linear regression to forecast the costs for its main product line. If fixed costs are equal to \(\$ 235,000\) and variable costs are \(\$ 10\) per unit, how many units does it need to sell at \(\$ 15\) per unit to make a \(\$ 300,000\) profit? a. 21,400 b. 47,000 c. 60,000 d. 107,000

Chapter 10

Reisen Travel offers helicopter service from sub-urban towns to John F. Kennedy International Airport in New York City. Each of its 10 helicopters makes between 1,000 and 2,000 round-trips per year. The records indicate that a helicopter that has made 1,000 round-trips in the year incurs an average operating cost of \(\$ 350\) per round-trip, and one that has made 2,000 round- trips in the year incurs an average operating cost of \(\$ 300\) per round-trip. 1\. Using the high-low method, estimate the linear relationship \(y=a+b X\), where \(y\) is the total annual operating cost of a helicopter and \(X\) is the number of round-trips it makes to JFK airport during the year. 2\. Give examples of costs that would be included in a and in \(b\). 3\. If Reisen Travel expects each helicopter to make, on average, 1,200 round- trips in the coming year, what should its estimated operating budget for the helicopter fleet be?

Chapter 10

\((\mathrm{CPA}, \text { adapted })\). The vertical axes of the graphs below represent total cost, and the horizontal axes represent units produced during a calendar year. In each case, the zero point of dollars and production is at the intersection of the two axes. Select the graph that matches the numbered manufacturing cost data (requirements 1-9). Indicate by letter which graph best fits the situation or item described. The graphs may be used more than once. 1\. Annual depreciation of equipment, where the amount of depreciation charged is computed by the machine-hours method. 2\. Electricity bill-a flat fixed charge, plus a variable cost after a certain number of kilowatt-hours are used, in which the quantity of kilowatt-hours used varies proportionately with quantity of units produced. 3\. City water bill, which is computed as follows: The gallons of water used vary proportionately with the quantity of production outputt 4\. cost of direct materials, where direct material cost per unit produced decreases with each pound of material used (for example, if 1 pound is used, the costis S10; if 2 pounds are used, the costis \$19.98 3 pounds are used, the cost is \(\$ 29.94\), with a minimum cost per unit of \(\$ 9.20\) 5\. Annual depreciation of equipment, where the amount is computed by the straight-line method. When the depreciation schedule was prepared, it was anticipated that the obsolescence factor would be greater than the wear-and- tear factor. 6\. Rent on a manufacturing plant donated by the city, where the agreement calls for a fixed-fee payment unless 200,000 labor-hours are worked, in which case no rent tis paid. 7\. Salaries of repair personnel, where one person is needed for every 1,000 machine-hours o o less (that is, 0 to 1,000 hours requires one person, 1,001 to 2,000 hours requires two people, and so on 8\. cost of direct materials used (assume no quantity discounts).) 9\. Rent on a manufacturing plant donated by the county, where the agreement calls for rent of \(\$ 100,000\) to be reduced by s1 for each direct manufacturing labor-hour worked in excess of 200,000 hours, but a minimum rental fee of \(\$ 20,000\) must be paid.

Chapter 10

What two assumptions are frequently made when estimating a cost function?

Chapter 10

A regression equation is set up, where the dependent variable is total costs and the independent variable is production. A correlation coefficient of 0.70 implies that: a. The coefficient of determination is negative. b. The level of production explains \(49 \%\) of the variation in total costs c. There is a slightly inverse relationship between production and total costs. A correlation coefficient of 1.30 would produce a regression line with better fit to the data.

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