Question

2. A welder and a carpenter decided to get out of the construction industry and build farm trailers instead. From building a few trailers on weekends, they estimated that the first trailer would take about $700 of their own labor to build and that an 85 percent learning rate can be anticipated on the cumulative average time as each trailer is built. (Note: They decided that their hourly wages should be no less than those they received in the construction trades.) The material costs for each trailer will be about $500, and the craftsmen do not see any way that this can be reduced. They estimate that each trailer can be sold for $1,000. In addition to making their wages on labor, they want to make 15 percent profit on the trailer materials. How many trailers must be built before this rate of profit can be realized

Answer 1

Answer:

Answer is explained in the explanation section below.

Explanation:

Data Given:

Material Cost Per Trailer = $500

Material Cost plus Profit Per Trailer (15%)  = $500 + 75 = $575

Selling Price = $1000

Labor Cost Remaining Per Trailer = $425

Formula to Calculate the number of Trailers:

X = X1 ($N^{S}$)

Where,

N = number of Trailers

S = Slope Parameter

X = $425

X1 = $700

So, First we need to find the slope parameter, in order to calculate the number of trailers to be built.

S = $\frac{log \alpha }{log 2}$

where, α = 0.85 rate of improvement.

Plugging in the values into the formula, we get:

S = $\frac{log (0.85) }{log 2}$

S = -0.234

Now, we can easily find the number of trailers.

X = X1 ($N^{S}$)

Plugging in the values,

425 = 700 x ($N^{-0.234}$)

Solving For N, we get:

N = 8.4 Trailers

N = 9 Trailers.

Hence, 9 Trailers must be built in order to realize this rate of profit.