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A manufacturer of pickles has a fixed monthly cost of
$10,000. Additionally, each jar of pickles that the manufacturer produces costs
$0.75. If these are the only monthly costs incurred by the manufacturer, which of the following functions best models the manufacturer's total monthly cost,
C, when it produces
p jars of pickles?
Choose 1 answer:
(A)
C(p)=10,000+0.75 p
(B)
C(p)=0.75+10,000 p
(C)
C(p)=10,000*0.75*p
(D)
C(p)=0.75(10,000+p

A manufacturer of pickles has a fixed monthly cost of $\$ 10,000$ . Additionally, each jar of pickles that the manufacturer produces costs $\$ 0.75$ . If these are the only monthly costs incurred by the manufacturer, which of the following functions best models the manufacturer's total monthly cost, $C$ , when it produces $p$ jars of pickles? $\newline$ Choose $1$ answer: $\newline$ (A) $C(p)=10,000+0.75 p$ $\newline$ (B) $C(p)=0.75+10,000 p$ $\newline$ (C) $C(p)=10,000 \cdot 0.75 \cdot p$ $\newline$ (D) $C(p)=0.75(10,000+p$

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Solve a system of equations using any method: word problems

Full solution

Q. A manufacturer of pickles has a fixed monthly cost of

\$ 10,000

. Additionally, each jar of pickles that the manufacturer produces costs

\$ 0.75

. If these are the only monthly costs incurred by the manufacturer, which of the following functions best models the manufacturer's total monthly cost,

C

, when it produces

p

jars of pickles?

\newline

Choose

1

answer:

\newline

(A)

C(p)=10,000+0.75 p

\newline

(B)

C(p)=0.75+10,000 p

\newline

(C)

C(p)=10,000 \cdot 0.75 \cdot p

\newline

(D)

C(p)=0.75(10,000+p

Understand Costs: Understand the fixed and variable costs. $\newline$ The manufacturer has a fixed monthly cost of $\$10,000$ , which does not change regardless of the number of jars produced. Additionally, there is a variable cost of $\$0.75$ for each jar of pickles produced. The total cost will be the sum of the fixed cost and the variable cost multiplied by the number of jars, $p$ .
Formulate Total Cost Function: Formulate the function for the total monthly cost. $\newline$ The total monthly cost, $C$ , is the sum of the fixed cost and the variable cost per jar times the number of jars, $p$ . This can be expressed as: $\newline$ $C(p) = \text{Fixed Cost} + (\text{Variable Cost per Jar} \times \text{Number of Jars})$ $\newline$ $C(p) = \$(10,000) + (\$(0.75) \times p)$
Match with Given Options: Match the formulated function with the given options. $\newline$ The function we formulated in Step $2$ is $C(p) = \$10,000 + (\$0.75 \times p)$ , which matches with option (A).

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