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Yuki888 [10]
3 years ago
5

Emarpy Appliances Inc. wants to determine the optimal production policy for their best selling refrigerator. The demand for this

has been relatively constant at about 8,000 each year. The production capacity for this product is limited to 200 units per day. Each time production starts, it costs the company $120 to move materials into place, reset the assembly line, and clean the equipment. The holding cost of a refrigerator is $50 per unit per year. Assume there are 250 working days per year. If Emarpy Inc wants to minimize the total annual inventory cost, how many refrigerators should be produced in each production run?
Business
1 answer:
monitta3 years ago
7 0

Answer:

Q' = 213.80

Explanation:

P(d): production rate per day = 200

Ic: Installation cost = 120

D: Demand = 8000

D(d): demand rate per day = 32

Uc: Unit cost (holding) = 50

Applying into Production order quantity model formula

Q'= \sqrt{\frac{2*D*Ic}{(1 - \frac{D(d)}{P(d)}) * Uc } }  = \sqrt{\frac{2*8000*120}{(1 - \frac{32}{200})*50 } }  = 213.80

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1) If 2 pounds of direct materials are used to make one unit of finished product, then 115,000 units × 2 lbs, or 230,000 lbs were used at $0.65 per lb of direct materials i.e. ($149,500 ÷ 230,000 lbs.).

The Formula for calculating Ending Direct Material Cost =  [Ending Direct Material Inventory * Cost per lb]

Therefore, Ending Direct Materials cost is 1,900 lbs. * $0.65 = $1,235.

2) Manufacturing Costs for 115,000 units  

   Variable Fixed Total

   Direct materials costs – $149,500  + Direct manufacturing labor costs – 31,500  + Plant energy costs – 3,000  + Indirect manufacturing labor costs

 

   (Variable + Fixed) i.e. 15,000+12,000 - 27,000  + Other indirect manufacturing costs

 

   (Variable + Fixed) i.e. 10,000+32,000 - 42,000

    So, Cost of goods manufactured - $253,000

Average unit manufacturing cost = $253,000 ÷ 115,000 units

                                                       = $2.20 per unit

Finished Goods Inventory at Dec. 31, 2014 = $15,400

Therefore Finished goods inventory total units = $15400 / $2.20

                                                                                = 7,000 units

3) Units sold in 2014 = Beginning inventory + Production – Ending inventory

                                   = 0 + 115,000 –7,000

                                 = 108,000 units

Therefore, Selling price in 2014 = Total Revenues / Units Sold

                                                      = $583,200 ÷ 108,000

                                                      = $5.40 per unit

4) Operating Income for 2014

            Revenues(108,000 units sold × $5.40) = $583,200

           Cost of units sold:

            Beginning finished goods, Jan. 1, 2014 = $0

            Cost of goods manufactured = $253,000

           Cost of goods available for sale = $253,000

           Ending finished goods, Dec. 31, 2014 = $15,400

           So, Cost of Units sold ($253000 - $15400) = $237,600

Therefore, Gross margin = Total Revenue - Cost of Units Sold

                                          = $583,200 - $237,600

                                         = $345,600

Operating costs:  Marketing, distribution, and customer-service costs

Variable + Fixed i.e. ($126,000 + $48,000) = $174,000

Administrative costs = $57000

Total Operating Costs = $231,000

Therefore Operating income for 2014 = $345600 - $231,000

                                                                = $114600

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