A firm has the following long run production function x = a(K^1/2)(L^1/2)(P^1/4), where a > 0 is a constant and K, L , P are inputs of the three factors. The prices of K, L , P are Rs. 1 , Rs. 9 and Rs. 8 respectively.

a) Derive the firm’s long run total cost function , long run average cost function and long run marginal cost function. Show the workings in detail

b) In the short run P is fixed and K and L are variable. Derive the firms short run a) Total Cost Function b) Variable Cost Function c) Average Variable Cost Function d) Marginal Cost Function.

c) Obtain an equation of the form P = f(x) showing the optimum quantity of the fixed factor P for the firm to acquire as a function of the intended output x.

Problem 4-14 Analysis of Work in Process T-account-Weighted-Average Method [LO4-1, LO4-2, LO4-3, LO4-4] Weston Products manufactures an industrial cleaning compound that goes through three processing departments—Grinding, Mixing, and Cooking. All raw materials are introduced at the start of work in the Grinding Department. The Work in Process T-account for the Grinding Department for May is given below: Work in Process—Grinding Department Inventory, May 1 188,670 Completed and transferred to the Mixing Department ? Materials 625,400 Conversion 353,320 Inventory, May 31 ? The May 1 work in process inventory consisted of 57,000 pounds with $114,570 in materials cost and $74,100 in conversion cost. The May 1 work in process inventory was 100% complete with respect to materials and 30% complete with respect to conversion. During May, 284,000 pounds were started into production. The May 31 inventory consisted of 100,000 pounds that were 100% complete with respect to materials and 60% complete with respect to conversion. The company uses the weighted-average method in its process costing system. Required: 1. Compute the Grinding Department's equivalent units of production for materials and conversion in May. 2. Compute the Grinding Department's costs per equivalent unit for materials and conversion for May. 3. Compute the Grinding Department's cost of ending work in process inventory for materials, conversion, and in total for May. 4. Compute the Grinding Department's cost of units transferred out to the Mixing Department for materials, conversion, and in total for May.

Compute the Grinding Department's equivalent units of production for materials and conversion in May.

Compute the Grinding Department's costs per equivalent unit for materials and conversion for May. (Round your answers to 2 decimal places.)

Compute the Grinding Department's cost of ending work in process inventory for materials, conversion, and in total for May. (Round your intermediate calculations to 2 decimal places.)

Compute the Grinding Department's cost of units transferred out to the Mixing Department for materials, conversion, and in total for May. (Round your intermediate calculations to 2 decimal places.)

Cain Components manufactures and distributes various plumbing products used in homes and other buildings. Over time, the production staff has noticed that products they considered easy to make were difficult to sell at margins considered reasonable, while products that seemed to take a lot of staff time were selling well despite recent price increases. A summer intern has suggested that the cost system might be providing misleading information.

The controller decided that a good summer project for the intern would be to develop, in one self-contained area of the plant, an alternative cost system with which to compare the current system. The intern identified the following cost pools and, after discussion with some plant personnel, appropriate cost drivers for each pool. There were:

In this particular area, Cain produces two of its many products: Standard and Deluxe. The following are data for production for the latest full year of operations.

The intern decides to look more closely at the manufacturing activity and determines that it can be broken down into two activities: production and engineering. Production covers the costs of ongoing manufacturing while engineering includes those activities dealing with engineering changes, design modifications, and so on.

The costs attributed to production are $5,412,000 and the costs attributed to engineering are $9,075,000. After discussion with plant engineers, the intern decides that the best cost driver for engineering is setups, because most of the work arises from changes in the way the product is run.

Required:

a-1. Compute the totals of the cost driver rates shown below.(Round intermediate calculations and "Manufacturing" answer to 2 decimal places.)

a-2. What unit product costs will be reported for the two products if the revised ABC system is used?(Round "Unit cost" answers to 2 decimal places.)

Suppose we have an Economic Order Quantity (EOQ) problem with discounts.

A (annual demand)= 10000, k (order cost)= 10, c1 (item cost)= 8, h (holding cost)= 0.1

For orders of 2000 or more, the cost is discounted from 8 to 7.3728.

What is the optimal TAC (total annual cost, including order and holding, and also including the purchase costs)?

Two children, each with a mass of 25.4 kg, are at fixed locations on a merry-go-round (a disk that spins about an axis perpendicular to the disk and through its center). One child is 0.72 m from the center of the merry-go-round, and the other is near the outer edge, 3.07 m from the center. With the merry-go-round rotating at a constant angular speed, the child near the edge is moving with translational speed of 12.0 m/s.

(a) What is the angular speed of each child? ω 0.72 m = rad/s ω 3.07 m = rad/s

(b) Through what angular distance does each child move in 5.0 s? θ 0.72 m = rad θ 3.07 m = rad

(c) Through what distance in meters does each child move in 5.0 s? d 0.72 m = m d 3.07 m = m (d) What is the centripetal force experienced by each child as he or she holds on? Fc, 0.72 m = N Fc, 3.07 m = N

(e) Which child has a more difficult time holding on?

1.The outer child has a more difficult time holding on.

2.The inner child has a more difficult time holding on

A) Relying STRICTLY on our classroom discussion: the US corporate tax rate was recently reduced from 35% to 21%. In the near future, would you expect the target (optimal) D/V ratios of US companies to increase or decrease as the result of this change? (2-3 sentences)

B) What LEGISLATIVE change (i.e. a law or a regulation), if adopted, would most likely cause the target (optimal) D/V ratios of US companies to move in the OPPOSITE direction compared to the one you predicted in part (A)? (2-3 sentences)

C) Relying STRICTLY on our classroom discussion: Assume US personal tax rates on capital gains will be reduced next month. In the near future, would you expect the propensity to pay dividends among US companies to increase or decrease as the result of this change? (2-3 sentences)

D) The need for financial flexibility is sometimes used as explanation for the tendency of US firms to utilize LOWER D/V ratios compared to the (optimal) target ratios based on the trade-off between tax benefits and distress- or agency-related drawbacks associated with debt financing. Give one argument for why the need for financial flexibility is likely NOT the reason for relatively low D/V ratio utilized by Walmart. (2-3 sentences)

Consider the following scenario:

The privately owned Baker Company was founded in 1960. The company manufactures kitchen cabinets and has been very successful, expanding from one facility to twelve facilities in the same and other states. All facilities but the original are located near interstate highways. The original facility, which is no longer the headquarters, is in a downtown area of a major city (which grew up around it) with relatively high real-estate taxes. It has had a negative contribution margin and a net loss for the last five years. The founder is retired and three of his children want to close the facility. The fourth does not, because it "was Dad's first place and I went there every day after school." She believes they can bring the facility back to profitability if the city's downtown revitalization project succeeds and they dedicate the first floor of the facility to retail.

Consider:

• Your definition for "negative contribution margin."
• Whether the fact that the facility is not near an interstate makes a difference in the decision.
• Would it make a difference if the company were publicly traded?
• Might there be additional costs, in addition to revenues, to convert the first floor of the facility to retail?
• What risks may be associated with leasing to retail stores?
• What is your recommendation? Close and sell the facility or modify the first floor to be able to lease to retail stores.

A study of fox rabies in a country gave the following information about different regions and the occurrence of rabies in each region. A random sample of

n₁ = 16

locations in region I gave the following information about the number of cases of fox rabies near that location.

x₁:

   Region I Data

A second random sample of

n₂ = 15

locations in region II gave the following information about the number of cases of fox rabies near that location.

x₂:

   Region II Data

(i) Use a calculator with sample mean and sample standard deviation keys to calculate x₁ and s₁ in region I, and x₂ and s₂ in region II. (Round your answers to two decimal places.)

(ii) Does this information indicate that there is a difference (either way) in the mean number of cases of fox rabies between the two regions? Use a 5% level of significance. (Assume the distribution of rabies cases in both regions is mound-shaped and approximately normal.)
(a) What is the level of significance?

Store Closing?

For this discussion, consider the following scenario:

The privately owned Baker Company was founded in 1960. The company manufactures kitchen cabinets and has been very successful, expanding from one facility to twelve facilities in the same and other states. All facilities but the original are located near interstate highways. The original facility, which is no longer the headquarters, is in a downtown area of a major city (which grew up around it) with relatively high real-estate taxes. It has had a negative contribution margin and a net loss for the last five years. The founder is retired and three of his children want to close the facility. The fourth does not, because it "was Dad's first place and I went there every day after school." She believes they can bring the facility back to profitability if the city's downtown revitalization project succeeds and they dedicate the first floor of the facility to retail.

• Your definition for "negative contribution margin."
• Whether the fact that the facility is not near an interstate makes a difference in the decision.
• Would it make a difference if the company were publicly traded?
• Might there be additional costs, in addition to revenues, to convert the first floor of the facility to retail?
• What risks may be associated with leasing to retail stores?
• What is your recommendation? Close and sell the facility or modify the first floor to be able to lease to retail stores.

On plant Mercury there is a special lake with two layers: dH2O and dHg (liquid mercury). The liquid water layer floats on top of the liquid mercury layer. Let ρH2O and ρHg denote the densities of water and mercury respectively. The gravitational field near the planet’s surface is gy, and the the atmospheric pressure near the surface of the lake P0.

a.Determine an expression in terms of the gi variables for the pressure in the lake as a function of depth all the way to the bottom of the layer of mercury. Graph this function.

b. Suppose an object density ρ is dropped into the lake. Assume ρH2O < ρ < ρHg. What fraction of the object you think will be submerged in the mercury after the object comes to rest in static equilibrium in the limit ρ → ρH2O .What fraction of the object you think will be submerged in the mercury after the object comes to rest in static equilibrium in the limit ρ → ρHg?

c.Determine an expression for ρ in terms of ρH 2O and ρHg that you believe would result in the object being half-submerged in the mercury layer and half-submerged in the water layer?Assume ρH2O < ρ < ρHg

d. Consider the general case where the density of the object is simply the unknown variable p. Determine an expression for the fraction of the object that will be submerged in the mercury when the object comes to rest in static equilibrium?