Q. 420 - Intermediate Algebra

Question

The manufacturer of a

granola bar spends \(1.20 to make

each bar and sells them for \)2. The

manufacturer also has fixed costs

each month of $8,000.(

a) Find the cost function C when x

granola bars are manufactured

(b) Find the revenue function R

when x granola bars are sold.

(c) Show the break-even point by

graphing both the Revenue and

Cost functions on the same grid.

(d) Find the break-even point.

Interpret what the break-even

point means.

Step-by-Step Solution

Answer

(a) Cost function $C=1.2x+8000$.

(b) Revenue function $R=2x$.

(c) 

The break-even point is $(10000,20000)$.

(d) Break-even point means the point above which product brings profit upon production.

Part (a) Step 1. Given information.

monthly fixed cost $=8000\$$

The cost incurred during production $=1.2\$$

The selling price of the product $=2\$$

Part (a) Step 2. Framing the equation.

The cost equation C will be the total cost incurred i.e 

Monthly $+$ cost incurred in one item

$=8000+1.2x$

for $x$number of item.

Part (b) Step 1. Given information.

monthly fixed cost $=\$8000$.

The cost incurred during production $\$1.2$

The selling price of the product $\$2$.

Part (b) Step 2. Framing the equation.

The revenue equation R will be the total revenue upon selling i.e 

$=2x$

for $x$ number of items.

Part (c) Step 1. Given information.

monthly fixed cost $\$8000$.

The cost incurred during production $\$1.2$

The selling price of the product $\$2$.

Part (c) Step 2. Graph

Part (d) Step 1. given information

monthly fixed cost $\$8000$.

The cost incurred during production $1.2

The selling price of the product $2.

Part (d) Step 2. Solution

Break-even point means the point above which product brings profit upon production. 

The break-even point is $(10000,20000)$.