Question

(Production Cost) Arthur, the manager of a furniture factory, finds that the cost of producing bookcases during the morning production shift is () = 2 + +500

dollars.
On a typical day, () = 25 bookcases are produced during the first hours of a production shift for 0 ≤ ≤ 5.
a. Express the production cost in terms of .
b. How much will have been spent on production by the end of the 3rd hour? What is the average cost of production during the first 3 hours?
c. Arthur’s budget allows no more than $11,000 for production during the morning shift. When will this limit be reached?

Answer 1

Say we consider the cost of production of q book cases during the morning production run is given by

(a) C(q) = q2 +q+500 observe that q(t) = 25 t bookcases are produced during the first t hours of a production run for 0<t<=5

To express the production cost in terms of t ,q(t)=25t into C(q) to get

C(q(t))= 25t2+25t+ 500

(b) C (t=3 hours) = 25*3 squared + 25*3 + 500 = $ 6200

(c) C(t=4 hours) = 25*4 squared + 25*4 +500= $ 10400

Now if we take t= 5 hours ,production cost goes beyond $11000 which is the budget for the morning shift.So the time limit is reached after 4 hours.