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?

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