Marla Payton

2021-12-27

A manufacturer of 24hr variable timers has a monthly fixed cost of 56000 and a production costs of 9 dollars for each timer manufactured the unit sell for 16 dollars each find the Break even point algebraically

zurilomk4

Beginner2021-12-28Added 35 answers

Step 1

Calculation:

Cost function$C\left(x\right)=56000+9x$ .

Revenue function$R\left(x\right)=16x$ .

The unit sell for 16 dollars.

Obtain the profit function as follows.

Profit function$P\left(x\right)=R\left(x\right)-C\left(x\right)$

$=16x-(56000+9x)$

$=16x-56000-9x$

$=7x-56000$

Step 2

Solving the break even point to equate the profit function as zero.

$7x-56000=0$

$7x=56000$

$x=\frac{56000}{7}$

$x=8000$

Thus, the break even point is (8000,0)

Step 3

Answer:

The break even point is (8000, 0).

Calculation:

Cost function

Revenue function

The unit sell for 16 dollars.

Obtain the profit function as follows.

Profit function

Step 2

Solving the break even point to equate the profit function as zero.

Thus, the break even point is (8000,0)

Step 3

Answer:

The break even point is (8000, 0).

Karen Robbins

Beginner2021-12-29Added 49 answers

If the units sell for $16, and cost $9 to produce; then the profit on each unit is $7. Let n be the number of units needed to break even. Then:

$7n=56000$

$n=8000\text{}{\textstyle \phantom{\rule{1em}{0ex}}}\text{or}{\textstyle \phantom{\rule{1em}{0ex}}}\text{}(16-9)n-56000=0$

So, the break-even point is 8000 units; and the break-even revenue is $12800

So, the break-even point is 8000 units; and the break-even revenue is $12800

karton

Expert2022-01-04Added 613 answers

The break even point occurs when the income from sales equals the cost to make the product

Let x = number of timers

cost = 5000 + 8x

Income = 13x

set them equal to find the break even point

5000+8x = 13x

5000 = 5x

x = 1000(so 1000 timers must be sold each month to break even

Profit

Profit = 0 at the break even point

So that is the point where it crosses the x axis

(1000, 0)

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