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

### Answer & Explanation

zurilomk4

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 $P\left(x\right)=R\left(x\right)-C\left(x\right)$
$=16x-\left(56000+9x\right)$
$=16x-56000-9x$
$=7x-56000$
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
The break even point is (8000, 0).

Karen Robbins

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: $7n=56000$ So, the break-even point is 8000 units; and the break-even revenue is$12800

karton

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 $=\text{Income}-\text{cost}$
Profit = 0 at the break even point
So that is the point where it crosses the x axis
(1000, 0)

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