A major auto manufacturer in Detroit, Michigan needs two types of seat assemblie
ID: 2563100 • Letter: A
Question
A major auto manufacturer in Detroit, Michigan needs two types of seat assemblies during 1998 on the following quarterly schedule:
Type 1
Type 2
First Quarter
25,000
25,000
Second Quarter
35,000
30,000
Third Quarter
35,000
30,000
Fourth Quarter
25,000
25,000
TOTAL
120,000
110,000
The excess seats from each quarter are carried over to the next quarter but are subject to an inventory-carrying charge of $20 per thousand seats. However, assume no inventory is carried over to 1999.
The company has contracted with an auto seat manufacturer that has two plants: One in Detroit and one in Toronto. Each plant can manufacture either type of seat; however, their maximum capacities and production costs are different. The production costs per seat and the quarterly capacity of each of the two plants in terms of number of seat assemblies is given as follows:
Quarterly Capacity
(total for the plant)
Production Cost
Type 1
Type 2
Detroit Plant
30,000
$225
$240
Toronto Plant
35,000
$165
$180
The packing and shipping costs from the two plants to the auto manufacturer are as follows:
Cost /100 seats
Detroit Plant
$15
Toronto Plant
$60
The problem is to determine a seat acquisition schedule from the two plants that minimizes the overall cost of these operations to the auto manufacturer for the year.
Type 1
Type 2
First Quarter
25,000
25,000
Second Quarter
35,000
30,000
Third Quarter
35,000
30,000
Fourth Quarter
25,000
25,000
TOTAL
120,000
110,000
Explanation / Answer
Answer to Question - There are two plants. One is Detroit Plant and Other is Toronto Plant. The cost comparison of 2 plants is shown below: Type 1 Type 2 Packaging Cost per seat Total Cost for Type 1 Total cost for Type 2 Detroit 225 240 0.15 225.15 240.15 Toronto 165 180 0.6 165.6 180.6 Difference in seat cost 59.55 59.55 From the above cost comparison, we understand that Toronto is manufacturing both the seats as a lower cost.The cost variance for both type of seat is $59.55. Thus, in case of any requirement the company should first purchase the seats from Toronto and remaining from Detroit, irrespective of type of seat as the cost variance is same for both the seats Schedule for Seat Purchase Purchase for Toronto considering capacity of 35000 seats per quarter Purchase for Detroit considering capacity of 30000 seats per quarter Particular Demand for Type 1 Demand for Type 2 Type 1 Type 2 Type 1 Type 2 First Quarter 25000 25000 25000 10000 NIL 15000 Second Quarter 35000 30000 35000 NIL NIL 30000 Third Quarter 35000 30000 35000 NIL NIL 30000 Fourth Quarter 25000 25000 25000 10000 NIL 15000 TOTAL 120000 110000 120000 20000 90000
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