1) Let, N Number of books produced for the year N 1,200,000) P Setup cost for a

ID: 1154778 • Letter: 1

Question

1) Let, N Number of books produced for the year N 1,200,000) P Setup cost for a single print run (P $5000) b Cost of producing a single book (b $1) c average monthly cost of storing a book (in dollars) (c-$0.01) x Number of print runs Fill in the missing entries in the table below using the letters x, N, P, b, and c. Cost Cate Information x print runs @SP per run N books $b per book Total for in dollars Setup Costs Production Costs Average Number of books in Stock per month Average number of books in stock per month @ Sc per month for 12 months Storage Costs Now add up the totals in the right-most column and thus create the total yearly cost function, C(x) b) C(x) Fill in) c) Determine any critical points of the cost function. SHOW WORK. Your answer should be of the form, x- expression, where "expression" is an expression involving one or more of the letters N, P, b, and c (not x)

Explanation / Answer

It is given that N: the number of books per year where N = 1,200,000

c= average monthly cost of storing a book in stock where c = $0.01

P= set up cost for a single print run where P=$5000

.b= cost of printing a single book where b= $1

And x = the number of print runs.

The cost function table can be filled up as follows:

Cost Category

Information

Total cost in $

Set up Cost

X print runs @$P/run

$Px = $5000*x

Production Cost

N books @$b per book

$Nb = $1,200,000*1 = $1,200,000

Average no. of books in stock per month

100,000

Storage Cost

Average no. of books in stock per month @ $c per month for 12 months

$Nc=$0.01*1,200,000 = $12,000

b) The total yearly cost(C(x)) will therefore be the summation of the total cost under each cost category such that

C(x) = Px + N*(b+c) (In $)

C(x) = $5000x+$1,200,000 + $12,000

Or C(x) = 1,212,000 + 5000x (in $)

c) Since the cost function is a linear one, there are two critical point on this cost function: the y-intercept and the x-intercept.

The value of the x-intercept when C(x) = 0 is x= -1,212,000/5000 = -242.4

Alternatively, the value of the x-intercept when C(x) = 0 is x= [-N(b+c)]/P

Thus the coordinate at this point is ([-N(b+c)]/P, 0) or (-242.4,0)

Similarly, for the y-intercept, x = 0 such that C(x) = N*(b+c) or C(x) = 1,212,000

Therefore the critical points are C(x) = N*(b+c) = 1,212,000 (which is independent of x as x=0)

And x= [-N(b+c)]/P = -242.4