West Calder Fabrication is trying to decide which of the following four cargo ships that should be used to ship their products, and has gathered the following information about each:

Cargo Ship Annual Fixed Cost Variable Cost (per unit)

American Integrity $40,000 $3

Sam Laud, $35,000 $5

Bums Harbor $30,000 $9

1. If West Calder has to ship 4,500 products annually, which cargo ship should West Calder use?

2. Over what range of storage levels would West Calder Fabrication prefer to use Sam Laud?

1. West Calder should use American since it is the cheapest with a cost of $53,500

2. The range of storage levels would West Calder Fabrication prefer to use Sam Laud is 1,250 to 2,500

Explanation:

1.

Determine the costs of shipping 4,500 units of products for each cargo ship

Step 1: American integrity

Total cost=Annual fixed cost + (cost per unit*number of units)

where;

Annual fixed cost=$40,000

Cost per unit=$3

Number of units=4,500 units

replacing;

Total cost=40,000 + (3*4,500) = 40,000+13,500=$53,500

American Integrity will cost $53,500

Step 2: Sam Laud

Total cost=Annual fixed cost + (cost per unit*number of units)

where;

Annual fixed cost=$35,000

Cost per unit=$5

Number of units=4,500 units

replacing;

Total cost=35,000 + (5*4,500) = 35,000+22,500=$57,500

Sam Laud will cost $57,500

Step 3: Bums Harbor

Total cost=Annual fixed cost + (cost per unit*number of units)

where;

Annual fixed cost=$30,000

Cost per unit=$9

Number of units=4,500 units

replacing;

Total cost=30,000 + (9*4,500) = 30,000+40,500=$70,500

Bums Harbor will cost $70,500

West Calder should use American since it is the cheapest with a cost of $53,500

2.

In order to use Sam Laud, Sam Laud's total cost should be less than or equal to American Integrity's cost.

35,000+5 n=40,000+3 n

40,000-35,000=5 n-3 n

2 n=5,000

n=5,000/2=2,500

n should be less or equal to 2,500

The minimum number of units that should be used in order to use Sam Laud can be determined as follows;

35,000+5 n=30,000+9 n

35,000-30,000=9 n-5 n

4 n=5,000

n=5,000/4=1,250

The range of storage levels would West Calder Fabrication prefer to use Sam Laud is 1,250 to 2,500