Your company just won a bid to provide 800000 electronic components to IBM, but

Question

Your company just won a bid to provide 800000 electronic components to IBM, but IBM is in a hurry. For every working day that goes by, the contract decreases in value by $300. It costs $180 to train each worker you use to assemble components and a well-trained worker can produce 5 components per day. A) Write a formula for the total reduction in value of the contract (including paying for workers) after t days. The reduction in value is dollars. B) How many workers should you use and how long will you take to fulfill the contract? It will take days to fulfill the contract. As a result, I should use workers. 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? It must be worth dollars.

Explanation / Answer

Hi :)

Reduction in value of the contract is given by the function R(t)=  300t+180(800000/(5t)) dollars. (300 dollars for each day of work, and 180 dollars dor every trained worker that can produce 5 components per day)

To minimize the reduction we need to differentiate this function with respect to t and equate it to zero;

Differentiating it with respect to t:
300- 180*800000/5t^2 =0;

5t^2= 480000; t^2=96000 which means t= 309.83 that is t=310 days (as in terms of the contract any portion of a day counts as a whole day) ; If 800000 products are to be produced in 310 days you need number of workers = 800000/ (310* 5)= 516.13 it means that you need 517 workers.

For the initial value of the contract to be at least break even it means that the total cost incurred due to reduction as the production process was delayed must be equal to the minimum worth of the cost;

Hence minimum worth for break even (MWB) = 300t+180(800000/(5t); Substituting t= 310 gives MWB= 185903.226 $
so, it must be worth 185903.226 dollars at least.

I hope it helps :)

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