Question

Ang company that produces pleasure boats has decided to expand one of its lines. The company is considering three Location alternatives. The cost structure for each location is given as shown in the table. Location LI L2 L3 Fixed Cost/yr 13,515 8,605 6,388 variable cost/unit 2.3 3.1 4.1 (Ex. In (Ex. In a) The range of output for location alternative 1 that would yield the lowest total cost is whole number, use Q, << >, >=to specify the range) b) The range of output for location alternative 2 that would yield the lowest total cost is whole number, use Q. << >, >= to specify the range) c) The range of output for location alternative 3 that would yield the lowest total cost is whole number, use Q, . - >> to specify the range) d) The alternative would yield the lowest total cost for an expected annual volume of 1505 boats is location (Ex. type in as L1, L2, or L3) ( En

Answer 1

Answer a: For L1 to be best:

Let the quantity = x

Total cost of L1 <= Total cost of L2 and L3

Total cost = fixed cost + quantity*variable cost

L1 = 13515 + 2.3*x

L2 = 8605 + 3.1*x

L3 = 6388 + 4.1*x

13515 + 2.3*x <= 8605 + 3.1*x

0.8*x >= 4910

x >= 6137.5

13515 + 2.3*x <= 6388 + 4.1*x

1.8*x >= 7127

x >= 3959.44

Q >= 6138 (rounded to nearest whole, if not required, leave accordingly)

Answer b: For alternative 2 to be best:

L1 = 13515 + 2.3*x

L2 = 8605 + 3.1*x

L3 = 6388 + 4.1*x

8605 + 3.1*x <= 13515 + 2.3*x

0.8*x <= 4910

x <= 6137.5

8605 + 3.1*x <= 6388 + 4.1*x

1*x >= 2217

x >= 2217

2217 <= Q <= 6138 (rounded to nearest whole, if not required, leave accordingly)

Answer c: For L3 to be best

L1 = 13515 + 2.3*x

L2 = 8605 + 3.1*x

L3 = 6388 + 4.1*x

6388 + 4.1*x <= 8605 + 3.1*x

1*x <= 2217

x <= 2217

6388 + 4.1*x <= 13515 + 2.3*x

1.8*x <= 7127

x <= 3959.44

Q <= 2217

Answer d: x = 1505

since, x =1505 comes in the range of L3,

The Alternative would yield the lowest total cost for an expected annual volume of 1505 boats is location L3.

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