The nutritionistof FLC Foods, Inc. designed a new product for everybody's consumption and believes that the variable cost in producing the said product is Php950.00 per unit and the fixed cost is Php60,000. Write the total cost as function of the product sold. If the selling for each product is Php1,700, how many units must be sold to break-even or to make somr profit.
number of units ---- x
cost = 950x + 60,000
we want
1700x ≥ 950x + 60000
750x ≥ 60000
x ≥ 80
At 80 units they break even, at more than 80 they make a profit
To write the total cost as a function of the product sold, we need to consider both the fixed cost and the variable cost per unit.
The variable cost per unit is given as Php950.00, so for each unit sold, we add Php950.00 to the total cost.
The fixed cost is given as Php60,000, which remains constant regardless of the number of units sold.
Therefore, the total cost (TC) can be represented as:
TC = (variable cost per unit * number of units sold) + fixed cost
= (Php950.00 * number of units sold) + Php60,000
To calculate the break-even point or the number of units needed to make a profit, we need to find the point where the revenue (selling price per unit multiplied by the number of units sold) equals the total cost.
Let's assume the selling price per unit is Php1,700. The revenue (R) can be represented as:
R = selling price per unit * number of units sold
= Php1,700 * number of units sold
Break-even point occurs when revenue equals the total cost (TC):
R = TC
Php1,700 * number of units sold = (Php950.00 * number of units sold) + Php60,000
To solve for the break-even point or the number of units needed to make a profit, we can rearrange the equation:
(R - TC) = 0
Php1,700 * number of units sold - (Php950.00 * number of units sold) - Php60,000 = 0
Php750.00 * number of units sold - Php60,000 = 0
Let's solve this equation to find the break-even point:
Php750.00 * number of units sold = Php60,000
number of units sold = Php60,000 / Php750.00
number of units sold = 80
Therefore, to break even or make a profit, FLC Foods, Inc. must sell at least 80 units of the new product.