Question

4. (Production Cost) Arthur, the manager of a furniture factory, finds that the cost of producing q bookcases during the morning production shift is C(a)= q +q +500 dollars. On a typical day,. q(t) = 25t bookcases are produced during the first t hours of a production shift for 0sts s a. Express the production cost C in terms of t How much will have been spent on production by the end of the 3d hour? What is b. 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? Hint: Study Section 1.1 of the textbook Page S of 6

Answer 1

(a) Consider the cost of producing q book cases during the morning production run is given by c(g) qq+500 Observe that g(t) 25t book cases are produced during the first t hours of a production run for 0stS5 To express the production cost C in terms of t to get Plug in C(())(25)25,+500 =625225t500 + C(t) 6252 25t +500, where 0s1S5 Therefore, the production cost C in terms of t is

(b) Consider С(4) -q +9+500 Plug3 in C(). Therefore, the total expense by the end of the 3rd hour is $6,200

To find the average cost of production during the first 3 hours as follows: C (3) q(3) 25(3) 6200 82.67 Therefore, the average cost of production during the first 3 hours is $82,67

(C) Consider C(g) q+500 Plug 4 in C(. to get C(4) 625(4)+25(4)+500 =10000100+500 =10600 Plug5 in C(t. to get C(5) 625(5)+25(5)+500 = 16250 - Observe that the budget is only $11,000; the limit will be reached at the beginning of the 5th year.