Solve the problem.
-Regrind, Inc. regrinds used typewriter platens. The variable cost to regrind each platen is $\$ 1.70$. The total cost to regrind 100 platens is $\$ 500$. Find the linear cost function to regrind platens. If reground platens sell for $\$ 8.10$ each, how many must be reground and sold to break even?
A) $C ( x ) = 1.70 x + 500 ; 79$ platens
B) $C ( x ) = 1.70 x + 330$; 34 platens
C) $\mathrm { C } ( \mathrm { x } ) = 1.70 \mathrm { x } + 330 ; 52$ platens
D) $C ( x ) = 1.70 x + 500$; 51 platens

Question

Quizplus · Accepted Answer

The total cost to regrind 100 platens is $500, which includes both variable and fixed costs. The variable cost per platen is $1.70, so the variable cost for 100 platens is $170 ($1.70 * 100). Subtracting this from the total cost ($500 - $170) gives the fixed cost of $330. Therefore, the cost function is $C(x) = 1.70x + 330$. To break even, revenue must equal cost. The revenue per platen is $8.10, so the break-even point is when $8.10x = 1.70x + 330$. Solving for $x$ gives the number of platens needed to break even, which is 52.

Solve the Problem $1.70\$ 1.70$1.70 the Total Cost to Regrind 100 Platens Is

Solve the Problem $\$ 1.70$ the Total Cost to Regrind 100 Platens Is