Find the profit equation of a business with a revenue equation of 2000x – 10×2 and a cost equation of 2000 + 500x.,
Answers
Answer:
Step 1: Set profit to equal revenue minus cost. For example, the revenue equation 2000x – 10x2 and the cost equation 2000 + 500x can be combined as profit = 2000x – 10x2 – (2000 + 500x) or profit = -10x2 + 1500x – 2000.
Step 2: Find the derivative of the profit equation (here’s a list of common derivatives). For example, the profit equation -10x2 + 1500x – 2000 becomes -20x + 1500.
Step 3: Set the equation equal to zero:
-20x + 1500 = 0
Step 4: Use algebra to find how many units are produced from the equation you wrote in Step 3.
20x = 1500
x = 75.
Step 5: Calculate the maximum profit using the number of units produced calculated in the previous step. In this example, inserting x = 75 into the profit equation -10x2 + 1500x – 2000 produces -10(75)2 + 1500(75) – 2000 or 54,250 in profit.
That’s how to find maximum profit in calculus.