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
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