The cost C and the revenue R for a brokerage firm depend on the number T of transactions executed. (Both C and R are measured in dollars.) It costs $730 per day to keep the office open, and brokers are paid an average of $25 per transaction. Also, $35 in fees are collected for each transaction. (a) Find a formula that gives C as a function of T. C(T) = (b) Find a formula that gives R as a function of T. R(T) = (c) Find the number of daily transactions that are needed to make the revenue $1200 more than the cost. 33 daily transactions

C(T) = $730 + $25T

R(T) = $35T

T = 193 transactions

Explanation:

Given that:

C = cost ; R = revenue ; T = number of transactions

Amount paid per transaction = $25

Cost keeping office open = $730

Amount collected on each transaction = $35

(a) Find a formula that gives C as a function of T.

C(T) = Cost of keeping office open + (cost per transaction × number of transactions)

C(T) = $730 + $25T

(b) Find a formula that gives R as a function of T.

R(T) = (Amount collected per transaction * number of transactions)

R(T) = $35T

(c) Find the number of daily transactions that are needed to make the revenue $1200 more than the cost.

R = C + 1200

Substitute the value of R and C into the equation:

35T = 730 + 25T + 1200

35T - 25T = 730 + 1200

10T = 1930

T = 1930 / 10

T = 193 transactions

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