Chains, Inc. is in the business of making and selling chains. Let c(t) be the nu
ID: 2881237 • Letter: C
Question
Chains, Inc. is in the business of making and selling chains. Let c(t) be the number of miles of chain produced after t hours of production. Let p(c) be the profit as a function of the number of miles of chain produced, and let q(t) be the profit as a function of the number of hours of production. (a) Suppose the company can produce three miles of chain per hour, and suppose their profit on the chains is $4000 per mile of chain. Find each of the following (include units). c(t) Meaning of c (t): p(c) (c) Meaning of p (c) g(t) q'(t) Meaning of g (t) How does t) relate to p (c) and c (t)?Explanation / Answer
(a) c(t)= miles of chain after t hrs.
p(t) = profit as number of miles of chain produced.
q(t) = number of hours of production
miles of chain per hour =3
profit per mile = $4000
c(t)= miles of chain = miles per hour * number of hours of production
c(t)= 3* q(t)
c '(t)= 3 * q' (t)
meaning of c'(t) = miles of chain per hour.
(b) p(t)= profit as a function of miles
=profit per mile * number of miles
=4000 c(t)
p '(t)= profit per unit mile
(c) q(t)= profit as number of hours produced
= profit/ mile * miles/hour
=4000 * 3
=12000
q(t) = profit is fixed ( $ 12000 per hour)
q '(t) = profit per unit hour=0 as q(t) id fixed quantity
relation between c'(t), p'(t) and q'(t)
profit per hour= profit per mile * miles per hour
q'(t) = p'(t) * c'(t)
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