The total fixed costs for manufacturing a product each month is $8,000. The vari

Question

The total fixed costs for manufacturing a product each month is $8,000. The variable cost per unit consists of direct labor, material and overhead. The labor will be based on the 25th unit and an 85% learning curve is expected to apply to the number of hours per unit. The first unit took 0.5 hours. Labor is charged at $18 per hour and overhead is charged at 150% of the direct labor. Material costs are $7.00 per unit. Marketing expects that the price of the product and the demand will be related such that p=$90-0.12D. Determine the optimal demand per month and the profit at that demand.

Explanation / Answer

The assumptions are given below

1 ) The fixed cost is $ 8,000

2) The material cost is $7.00 per unit

3) the calculation of labor cost , time to be considered is 25 unit at 85 learning curve is 0.470 and the first unit time to produce is 0.50 hours is given , then the time to produce 1 unit at 85% learning curve at 25th unit is = 0.50 x 0.47 is 0.235 hours

4 ) the direct labor cost is $ 18 x0 .235 = $4.23

5 ) the overhead cost is 150% of $ 4.23 , which is $6.345

The total variable cost will be $ 7 + $ 4.23 + $ 6.345 = $17.575

The optimal demand as per equation is p=$90-0.12D.

Where putting values

P = $17.575

$17.575 = $ 90 – 0.12D

0.12D = 90 – 17.575

D = 72.425 /0.12

D= 603 units round off

The profit will be at this demand

Revenue = 603 x 90 = $54,270

Fixed cost = $ 8,000

Variable Cost = 603 x 17.575 = $ 10,597

Profit is $ 54,270 - $8,000 - $ 10,597 is $ 35,673

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