Find the average rate of change illustrated in the graph.
-Regrind, Inc. regrinds used typewriter platens. The variable cost to regrind each platen is $1.30. The total cost to regrind 110 platens is $500. Find the linear cost function to regrind platens. If reground platens sell for $9.60
Each, how many must be reground and sold to break even?
A) $C ( x ) = 1.30 x + 500 ; 46$ platens
B) $C ( x ) = 1.30 x + 357 ; 43$ platens
C) $C ( x ) = 1.30 x + 500$; 61 platens
D) $\mathrm { C } ( \mathrm { x } ) = 1.30 \mathrm { x } + 357 ; 33$ platens

Question

Find the average rate of change illustrated in the graph.
-Regrind, Inc. regrinds used typewriter platens. The variable cost to regrind each platen is $1.30. The total cost to regrind 110 platens is $500. Find the linear cost function to regrind platens. If reground platens sell for $9.60
Each, how many must be reground and sold to break even? 
A) $C ( x ) = 1.30 x + 500 ; 46$ platens
B) $C ( x ) = 1.30 x + 357 ; 43$ platens
C) $C ( x ) = 1.30 x + 500$; 61 platens
D) $\mathrm { C } ( \mathrm { x } ) = 1.30 \mathrm { x } + 357 ; 33$ platens

Quizplus · Accepted Answer

The cost function $C(x) = 1.30x + b$, where $b$ is the fixed cost and $x$ is the number of platens. To find $b$, we use the total cost for 110 platens: $500 = 1.30(110) + b$. Solving for $b$ gives $b = 500 - 143 = 357$, so $C(x) = 1.30x + 357$. To break even, revenue $R(x) = 9.60x$ must equal cost $C(x)$, so $9.60x = 1.30x + 357$. Solving for $x$ gives the number of platens needed to break even, which is 43.

Find the Average Rate of Change Illustrated in the Graph C(x)=1.30x+500;46C ( x ) = 1.30 x + 500 ; 46C(x)=1.30x+500;46

Find the Average Rate of Change Illustrated in the Graph $C ( x ) = 1.30 x + 500 ; 46$