Your company just won a bid to provide 600000 electronic components to IBM, but

Question

Your company just won a bid to provide 600000 electronic components to IBM, but IBM is in a hurry. For every working day that goes by, the contract decreases in value by $500. It costs $200 to train each worker you use to assemble components and a well-trained worker can produce 15 components per day.

A) Write a formula for the total reduction in value of the contract (including paying for workers) after t days.

B) How many workers should you use and how long will you take to fulfill the contract? (Note: in terms of the contract any portion of a day counts as a whole day.)

C) What must the initial value of the contract be in order for it to be at least break even for your company after the optimal number of days?

Explanation / Answer

A) Reduction in value = Reduction rate decrement * time + Cost of Training the work * (number of electronic components/(components produced per day * t))

=> 500t + 200 * (600000/15t)

=> 500t + 8000000/t

b)

For finding the least reduction value, we need to take the derivative of redution function

R'(t) = 500 - 8000000/t^2

Equating the derivative to zero we get

Hence the value of t comes to be 126.49

So the number of days will be 127 days

Number of workers = 600000/(127*15) = 314.96

Hence we need atleast 315 workers

c) The data is insufficient to solve the problem, since for break even, we need to estimate the overall cost

Overall Cost of workers = 315 * 200 = 63000

But there is no information about the raw material hence information is less

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