An ondemand publisher charges 2250 to print a 600 page book

An on-demand publisher charges $22.50 to print a 600 page book and $15.50 to print a 400 page book. Find a linear function which models the cost of a book C as a function of the number of pages p. Interpret the slope of the linear function and find and interpret C(0).

Solution

publisher charges $22.50 to print a 600 page book and $15.50 to print a 400 page book.

(p₁,C₁)=(600,22.5),(p₂,C₂)=(400,15.5)

equation of line in 2 point form passing through (x1,y1) ,(x2,y2) is y-y₁=[(y₂-y₁)/(x₂-x₁)]*(x-x₁)

C-C₁=[(C₂-C₁)/(p₂-p₁)]*(p-p₁)

C-22.5=[(15.5-22.5)/(400-600)]*(p-600)

C-22.5=(7/200)*(p-600)

C-22.5=(7/200)p- ((7/200)*600)

C-22.5=0.035p- 21

C=0.035p- 21+22.5

C=0.035p+ 1.5

slope of the linear function =0.035

C(0) =0.035*0+1.5

C(0) = 1.5

slope of the linear function says that cost increases by 0.035$ to print each additional page.

C(0) =1.5$ says that minimum additional charge to print the book which is independant of number of pages prited