Question

a small business makes cookies and sells them at the farmers market. the fixed monthly cost for use of a health department - approved kitchen and rental space at the farmers market is $720. the cost of labour, taxes, and ingredients for the cookies amounts to $0.23 per cookie, and the cookies sell for $7 per dozen.
part 1 of 5
(a) write a linear cost function representing the cost c(x) to produce x dozen cookies per month.
the linear cost function is c(x)=
part 2 of 5
(b) write a linear revenue function representing the revenue r(x) for selling x dozen cookies.
the linear revenue function is r(x)=

Explanation:

Step1: Define cost function components

Fixed cost = $\$720$, variable cost per dozen: $\$0.23 \times 12 = \$2.76$

Step2: Build linear cost function

$C(x) = \text{Fixed Cost} + \text{Variable Cost} \times x$
$C(x) = 720 + 2.76x$

Step3: Define revenue function components

Revenue per dozen = $\$7$

Step4: Build linear revenue function

$R(x) = \text{Price per dozen} \times x$
$R(x) = 7x$

Answer:

(a) $C(x) = 720 + 2.76x$
(b) $R(x) = 7x$