On October 23, 2001, Apple released the first iPod. To date, Apple has sold over

Question

On October 23, 2001, Apple released the first iPod. To date, Apple has sold over 269,000,000 iPods and counting. The iconic white earphones shipped with every iPod are manufactured solely by Fostex in Japan. A Fostex engineer is considering a new machine to manufacture the box containing the earphones when they are shipped to the customers. Use the graph to answer the question. If the selling price was increased by $1 per box, how many boxes would need to be produced for Machine #2 to breakeven? A. 6 times 10^6 boxes B. 3 times 10^7 C. 1.3 times 10^7 D. Machine #2 would breakeven at a point more than 5 times 10^7 boxes

Explanation / Answer

option D is right

let y denote the parameter on y-axis and x denote the parameter on x-axis

then slope of line equal to the per box cost of each machine

now equation of breakeven line is

y=mx where m= (3-0)/(2-0)=3/2=1.5 thus y=1.5x

equation of machine 2 graph

(y-1)/(x-0)= (3-1)/(2-0) =1 thus y -1 = x y=1+x

above equation is in the form of y=mx+c where m= 1 which is cost of per box

now cost increases by 1 hence new m=2

now equation of machine 2 line will be y=2x+1

intersection of this line with breakeven line is can be calculated by solving 2 simul taneously eqution

thus y=1.5 x and y=2x+1 solving these two

1.5x=2x+1 x=-2   

thus there will no intersection of these 2 line upto 5*107 boxes

hence option D is right

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