Schmutz Auto Wash provides car washes. Its production function is ? = 2?^1/2(? - 1)^1/2
where ? is cars washed per day, ? is daily hours of labor input, and ? is daily usage of capital inputs. The price of a unit of capital input is $48. The price of a unit of labor input is $16. In the short run, Schmutz has 4 units of capital input installed (so ? = 4).

a). Find Schmutz’s short run daily total cost function, short run daily variable cost function, and short run daily fixed costs.

b). Find Schmutz’s short run marginal cost function, short run average variable cost function, and short run total cost function.

c). Suppose that the market for car washes is perfectly competitive and the going market price of a car wash is ?. Find Schmutz’s short run daily supply function, including its shutdown price.

d). Find Schmutz’s short run daily quantity supplied, producer surplus, and profit if ? = 40.

(Calculating FIFO, Weighted Average Cost—Periodic) The following information is for the inventory of mini-kettles at Funnell Company Limited for the month of May:

Instructions

a. Assuming that the periodic inventory method is used, calculate the inventory cost at May 31 under each of the following cost flow formulas:

• 1. FIFO
• 2. Weighted average (round the weighted average unit cost to the nearest one tenth of one cent)

b.  Which method will yield the higher current ratio or gross profit?

Weighted Average Method, Unit Costs, Valuing Inventories

Walser Inc. produces a product that passes through two processes. During February, equivalent units were calculated using the weighted average method:

The costs that Walser had to account for during the month of February were as follows:

1. Using the weighted average method, determine unit cost. If required, round your answer to the nearest cent and use rounded amount in subsequent requirements.

2. Under the weighted average method, what is the total cost of units transferred out? What is the cost assigned to units in ending inventory? If required, round your answers to the nearest dollar.

Cost of units transferred out: $

Cost of ending inventory: $

Jordan Company currently is using a plant-wide factory overhead rate based on machine hours. The budgeted factory overhead costs is $405,000. Company has two departments, X and Y. Company is considering use of departmental overhead rates for the allocation of each departments’ overhead costs to jobs. Overhead would be applied based on direct labor cost in Department X and machine-hours in Department Y. The following additional information is available:

Budgeted Amounts                           Department X           Department Y

Direct labor cost                                          $180,000                     $165,000

Factory overhead                                         $225,000                     $180,000

Machine-hours                                           51,000 mh                   40,000 mh

Actual data for Job #10                   Department X           Department Y

Direct materials requisitioned                        $10,000                      $16,000

Direct labor cost                                            $11,000                       $14,000

Machine-hours                                             5,000 mh                     3,000 mh

1. Compute total cost of manufacturing Job 10 under current system (using plant-wide rate).

2. Compute total cost of manufacturing Job 10 using departmental overhead rates.

Assembly Department uses a process cost accounting systm and a weighted-average cost flow assumption. The department adds minerals at the beginning of the process and incur conversion costs uniformly throughout the process. During July, $190,000 of materials cost and $135,000 in conversion costs were charged to the department. The beginning work in process inventory was $93,000 on July 1, comprised of $80,000 of materials costs and $13,000 of conversion costs.

Other Data for the month of July are as follows:
Beginning work in process Inventory 7/1    25,000 units (40% complete)
Units completed and transferred out. 90,000 units
Ending work in process inventory 7/31       30,000 units (30% complete)

Instructions
1. How many physical units have to be accounted for in July?
2. What are the equivalent units of production for materials and for conversion costs for the month of July?
3. What is the total cost assigned to the 90,000 units that were transferred out of the process in July?
4. What is the remaining total cost of inventory within the Assembly department as of July 31?

Allegiant Airlines charges a mean base fare of $86. In addition, the airline charges for making a reservation on its website, checking bags, and inflight beverages. These additional charges average $35 per passenger. Suppose a random sample of 80 passengers is taken to determine the total cost of their flight on Allegiant Airlines. The population standard deviation of total flight cost is known to be $38. Use z-table.

a. What is the population mean cost per flight?
$

b. What is the probability the sample mean will be within $10 of the population mean cost per flight (to 4 decimals)?

c. What is the probability the sample mean will be within $5 of the population mean cost per flight (to 4 decimals)?

Suppose a random sample of size 41 is selected from a population with = 12. Find the value of the standard error of the mean in each of the following cases (use the finite population correction factor if appropriate).

1. The population size is infinite (to 2 decimals).
   
   
2. The population size is N = 50,000 (to 2 decimals).
   
   
3. The population size is N = 5,000 (to 2 decimals).
   
   
4. The population size is N = 500 (to 2 decimals).

Coverall Inc. produces and sells a unique type of case for a standard-size tablet computer that is guaranteed waterproof but still allows for regular functionality of the tablet. The company has just opened a new plant to manufacture these cases, and the following cost and revenue data have been provided for the first month of the plant’s operation in the form of a worksheet:

Since the new case is unique in design, management is anxious to see how profitable it will be and has asked that an income statement be prepared for the month.

Prepare a contribution format income statement for the month. (Do not leave any empty spaces; input a 0 wherever it is required.)

1. Assume that your widget manufacturing company has a total annual demand of N widgets per year evenly distributed across the year. Each widget cost $b dollars in material and manufacturing costs to make. Every time you do a production run to make some widgets, you incur a set-up cost of P dollars. Any widgets awaiting sale must be stored and thus incur an average storage fee of c dollars per widget per year. Let x be the size of each production run (i.e. x is the number of widgets per production run).

1. Write a cost function C(x) and explain each term in the equation and how it was determined.
2. Write down any constraints on the allowable values of x.
3. Determine a formula for the value of x that minimizes total annual cost. Show all of your work.
4. Prove that your formula actually corresponds to the global minimum cost.
5. Write down a formula for the number of production runs per year as a function of x.

The 501st is exploring the possibility of purchasing a van to transport their Stormtroopers and other members to gigs outside of the Memphis area to such events as Weird Al concerts. The agreed cost of the van that they have decided to purchase is $45,000 which includes a rear lift to get Brodie and his equipment in and out of the van. Mr. Dan Dan has offered financing at an interest rate of 8% per year over a total of five years. The financing arrangement requires a down payment now of 25% of the initial cost. Compute the cost per year to finance the van over the five year loan. The 501st believes that they will keep the van for a total of ten years. They plan to sell the van for $7,000 after ten years of use. The operating and maintenance cost of the van is expected to be $450 per year. If the 501st uses a Minimum Attractive Rate of Return (MARR) of 6% per year, what is the annual owning cost to the nearest cent per year over the ten-year life of the van? Include a cash flow diagram with your solution.

about company, the purchasing operation 4 hours are need to process a purchase order, regardless of the quantity purchased. Salaries in the Purchasing Department average 12 dollar per hour, including employee benefits. a detailed analysis of 30 previous purchase orders showed that 400 dollar  was spent on calling , paper, and other consumables directly related to the ordering process and a holding cost of 15%

annual demand is 6000 units, and the plant operates 240 days per year, the company has a contract to purchase from the supplier at a cost of 40 dollar per unit, and it is using a policy of replenishing its inventory of compressors once a month.. Service level indicate that 0.7 stockouts per year is acceptable

1_find reorder cost ?

2_ find current annual total inventory cost under the company’s current policy

3_Find the optimal order quantity.

4_How much safety stock is recommended for the company to carry?

5_find optimal total annual inventory cost?

6_ How much savings does the Company achieve by implementing the optimal policy?