Your company just won a bid to provide 400000 electronic components to IBM, but
ID: 2882117 • Letter: Y
Question
Your company just won a bid to provide 400000 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 $350 to train each worker you use to assemble components and a well-trained worker can produce 15 components per day. 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. 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. 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
From the given question,
Total components=400000
every day contract decreases by =$500
Training cost = $350
components produced by each worker= 15
(a)suppose you train x workers.
and they work for t days.
total components produced = 15xt = 400000
x= (400000/15t)
Total reduction in value of contract (R)= 500t + 350 (400000/15t)
(b)for reduction in value of contract be minimum, its derivative should be zero.
dR/dt=0
500 - (350 x 400000/15)(1/t2)=0
t2= (350 x 400000/15)/500
t=136.6days
t=137 days
Number of workers= (400000/(15 x 137))=194.6
=195 workers
c)for breakeven, total revenue= total cost
=500t + 350 (400000/15t)
=500(137) + 350(400000/(15x137))
=$136626.5
so, initial value of contract should be worth $136627.( to nearest dollar)
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.