Find the average rate of change illustrated in the graph.
-Regrind, Inc. regrinds used typewriter platens. The variable cost to regrind each platen is $\$ 1.90$. The total cost to regrind 100 platens is $\$ 300$. Find the linear cost function to regrind platens. If reground platens sell for $\$ 8.70$ each, how many must be reground and sold to break even?
A) $C ( x ) = 1.90 x + 110 ; 11$ platens
B) $C ( x ) = 1.90 x + 110 ; 17$ platens
C) $C ( x ) = 1.90 x + 300 ; 29$ platens
D) $C ( x ) = 1.90 x + 300 ; 45$ platens

Question

Quizplus · Accepted Answer

The cost function is found by using the given variable cost per platen (\$1.90) and the total cost for 100 platens (\$300). The fixed cost is found by subtracting the variable cost for 100 platens from the total cost: $300 - (100 \times 1.90) = $110. Thus, the cost function is $C(x) = 1.90x + 110$. To break even, the revenue from selling the platens must equal the cost of regrinding them. Setting the revenue function equal to the cost function and solving for $x$ gives the break-even point. The revenue per platen is \$8.70, so the equation is $8.70x = 1.90x + 110$. Solving this equation for $x$ gives the number of platens needed to break even, which is 17.

Find the Average Rate of Change Illustrated in the Graph $1.90\$ 1.90$1.90

Find the Average Rate of Change Illustrated in the Graph $\$ 1.90$