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Mathematics

Cost Function

  1. Regrind, Inc. reginds used typewriter platens. The cost to buy back each used platen is $2.60. The fixed cost to run the grinding machine is $195 per day. If the company sells the regroundplatens for $7.60, write a cost function, a revenue function, and determine how many platens must be reground daily to break even? (Assume that there are no unsold platens at the end of the day.)
    (a) Express the Cost C as a function of x.
    C(x)=
    (b) Express the Revenue as a function of x.
    R(x)=
    (c) Determine analytically the value of x which revenue equals cost.

(a)

Where x represents the number of days and p represents each individual platen, the cost is represented as follows:

C(x) = $195x + $2.60p

(b)

Where x represents the number of days and p represents each individual platen, the revenue is represented as follows: