Suppose a firm manufactures hand towels and sells them for P75 each. If the cost incurred in the production and sale of the hand towels are P200,000 plus P25 for each hand towel produced and sold.
FIND THE:
A. Revenue Function, Cost Function and Profit Function.
B. How much is the revenue, cost, profit of the company if they sold 100 hand towels?
C. Find the break-even point and sales.
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A. To find the revenue function, cost function, and profit function, we need to define the variables involved:
Let x represent the number of hand towels produced and sold.
Let R(x) represent the revenue function.
Let C(x) represent the cost function.
Let P(x) represent the profit function.
1. Revenue Function (R(x)):
The revenue generated from selling hand towels is given by the selling price multiplied by the quantity sold. In this case, the selling price per hand towel is P75. Therefore, the revenue function is:
R(x) = 75x
2. Cost Function (C(x)):
The cost incurred in the production and sale of the hand towels consists of two components: a fixed cost and a variable cost. The fixed cost is given as P200,000, and the variable cost is P25 per hand towel produced and sold. Therefore, the cost function is:
C(x) = 200,000 + 25x
3. Profit Function (P(x)):
The profit can be calculated by subtracting the cost from the revenue:
P(x) = R(x) - C(x)
P(x) = 75x - (200,000 + 25x)
P(x) = 50x - 200,000
B. If the company sold 100 hand towels, we can calculate the revenue, cost, and profit:
Revenue (R):
R(100) = 75 * 100 = P7,500
Cost (C):
C(100) = 200,000 + 25 * 100 = P202,500
Profit (P):
P(100) = 50 * 100 - 200,000 = -P150,000
Therefore, the revenue is P7,500, the cost is P202,500, and the profit is -P150,000.
C. The break-even point is reached when the profit is zero, indicating that the company neither makes a profit nor incurs a loss. To find the break-even point, we set the profit function equal to zero and solve for x:
P(x) = 50x - 200,000 = 0
50x = 200,000
x = 4,000
So, the break-even point is reached when the company sells 4,000 hand towels.
To find the sales at the break-even point, we substitute the value of x (4,000) into the revenue function:
R(4,000) = 75 * 4,000 = P300,000
Therefore, the break-even point is 4,000 hand towels, and the sales at the break-even point are P300,000.