regrind, inc. regrinds used typewriter platens. the cost per platen is $2.70. the fixed cost to run the…

regrind, inc. regrinds used typewriter platens. the cost per platen is $2.70. the fixed cost to run the grinding machine is $243 per day. if the company sells the reground platens for $5.70, how many must be reground daily to reach the break - even point?\n\na. 54 platens\nb. 28 platens\nc. 90 platens\nd. 81 platens

regrind, inc. regrinds used typewriter platens. the cost per platen is $2.70. the fixed cost to run the grinding machine is $243 per day. if the company sells the reground platens for $5.70, how many must be reground daily to reach the break - even point?\n\na. 54 platens\nb. 28 platens\nc. 90 platens\nd. 81 platens

Answer

Explanation:

Step1: Set up cost and revenue equations

Let $x$ be the number of platens reground. Cost $C = 2.7x+243$, Revenue $R = 5.7x$.

Step2: Set cost equal to revenue for break - even

$2.7x + 243=5.7x$.

Step3: Solve for $x$

Subtract $2.7x$ from both sides: $243 = 5.7x-2.7x$, so $243 = 3x$. Then $x=\frac{243}{3}=81$.

Answer:

D. 81 platens