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A welder and a carpenter decided to transition from the construction industry to building farm trailers. After building a few trailers on weekends, they estimated that the first trailer would require $700 of their own labor, with an 85 percent learning rate anticipated on the cumulative average time for each subsequent trailer. The material costs for each trailer are estimated to be $500, with no anticipated reduction. Each trailer can be sold for $1,000.

The craftsmen aim to ensure their hourly wages are equivalent to those in the construction trades, and they also want to achieve a 15 percent profit on the trailer materials.

How many trailers must be built before this rate of profit can be realized?

Answer :

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 ([tex]N^{S}[/tex])

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 = [tex]\frac{log \alpha }{log 2}[/tex]

where, α = 0.85 rate of improvement.

Plugging in the values into the formula, we get:

S = [tex]\frac{log (0.85) }{log 2}[/tex]

S = -0.234

Now, we can easily find the number of trailers.

X = X1 ([tex]N^{S}[/tex])

Plugging in the values,

425 = 700 x ([tex]N^{-0.234}[/tex])

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.

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Rewritten by : Barada