If the demand function=9000-30p and the cost function=90000+30x then find break even point
CALCULUS FOR ECONOMICS QUESTION AND ANSWER
revenue = price * quantity
break-even is when revenue = cost
Tr=P*Q
Work this question
To find the break-even point, you need to determine the quantity (Q) at which the total revenue equals the total cost. In other words, you need to find the quantity at which the demand function (revenue) is equal to the cost function.
Given that the demand function is 9000 - 30p and the cost function is 90000 + 30x, we need to find the values of p and x that make these two equations equal.
Since the demand function is in terms of price (p) and the cost function is in terms of quantity (x), we first need to express one of the variables in terms of the other. In this case, let's express p in terms of x using the demand function.
Demand function: 9000 - 30p
To find p, we can rearrange the equation as follows:
30p = 9000 - x
p = (9000 - x) / 30
Now, substitute this expression for p into the cost function:
Cost function: 90000 + 30x
Revenue (R) can be calculated as the product of price (p) and quantity (x):
R = p * x
R = ((9000 - x) / 30) * x
To find the break-even point, we set the revenue equal to the cost function:
R = Cost
((9000 - x) / 30) * x = 90000 + 30x
Now we solve this equation to find the value of x, which represents the break-even point.
((9000 - x) / 30) * x = 90000 + 30x
Multiply both sides by 30 to eliminate the fraction:
x^2 - 1000x = 2700000 + 900x
Rearrange the equation to get it in standard quadratic form:
x^2 - 1900x - 2700000 = 0
Now we can solve this quadratic equation using factoring, completing the square, or the quadratic formula. Once you solve for x, you will have the break-even point quantity.