The labor cost to produce a certain item is $8.50 per hour. Job setup costs $50 and material costs are $20 per unit. The item can be purchased for $88.50 per unit. The learning rate is 90 percent. Overhead is charged at a rate of 50 percent of labor, materials, and setup costs. Required:
a. Determine the average unit cost for 20 units, given that the first unit took 5 hours to complete.
b. What is the minimum production quantity necessary to make production cost less than purchase cost?

Explanation:

Given

Setup cost =$50

Material cost = $20

= $20×$20

= $400

Purchased cost = $88.50

Learning rate (P) = 90%

Labor cost is $8.50, and it requires 5 hours to produce the first unit. Total time required for the production of 20 units is

= 5×14.608

= $73.04

The value 14.608 is the total time factor which has been taken from table 7S.1 and the time required for the production of 20 units at the rate of 90% is 14.608. Hence, the labor cost for the production of 20 units will be calculated using the following method.

Cost of labor for production of 20 units

= 8.50×73.04

= $620.84

Hence,

In the problem, it has been given that the overhead cost is 50% of the labor material, and setup cost. Hence,

= 50/100 (620.84+50+400)

= 0.5×(1070.84)

= $535.42

Hence total cost

$535.42 +$1070.84

=$ 1606.26

Hence, the cost of production of 20 units is calculated by the following method.

= $1606.26÷20

=$80.313

Therefore, the unit cost is $80.313/unit.

Ans B:

The minimum production quantity important to make the production cost less than the purchase cost is calculated by the trial-and-error method. Now, let's take average unit cost when the 10 units are produced.

Setup cost =$50

Material cost = $20

= $20×$10

= $200

Labor cost is $8.50, and it requires 5 hours to produce the first unit. Total time required for the production of 10 units is

=5×7.994

= $39.97

The value 7.994 is the total time factor which has been taken from table 7S.1 and the time required for the production of 10 units at the rate of 90% is 7.994. Therefore, the labor cost for the production of 10 units will be calculated by the following method.

The cost of production of 20units

8.50×7.994×5

= $339.745

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