Question

For a company, the cost of producing x items is 35x + 300, and the revenue for selling x items is 75x - 0.5x^2. Part 1) Set up an expression for the profit from producing and selling x items. The profit from producing and selling x items can be calculated by subtracting the cost from the revenue. Therefore, the expression for the profit is: Profit = Revenue - Cost Profit = (75x - 0.5x^2) - (35x + 300) Profit = 75x - 0.5x^2 - 35x - 300 Profit = -0.5x^2 + 40x - 300 Part 2) Find two values of x that will show a profit of $300. To find the values of x that will result in a profit of $300, we need to set the profit expression equal to 300 and solve for x. -0.5x^2 + 40x - 300 = 300 -0.5x^2 + 40x - 600 = 0 Part 3) Is it possible for the company to make a profit of $15,000? To determine if the company can make a profit of $15,000, we need to set the profit expression equal to 15,000 and solve for x. -0.5x^2 + 40x - 300 = 15,000 -0.5x^2 + 40x - 15,300 = 0

          For a company, the cost of producing x items is 35x + 300, and the revenue for selling x items is 75x - 0.5x^2.

Part 1) Set up an expression for the profit from producing and selling x items.
The profit from producing and selling x items can be calculated by subtracting the cost from the revenue. Therefore, the expression for the profit is:
Profit = Revenue - Cost
Profit = (75x - 0.5x^2) - (35x + 300)
Profit = 75x - 0.5x^2 - 35x - 300
Profit = -0.5x^2 + 40x - 300

Part 2) Find two values of x that will show a profit of $300.
To find the values of x that will result in a profit of $300, we need to set the profit expression equal to 300 and solve for x.
-0.5x^2 + 40x - 300 = 300
-0.5x^2 + 40x - 600 = 0

Part 3) Is it possible for the company to make a profit of $15,000?
To determine if the company can make a profit of $15,000, we need to set the profit expression equal to 15,000 and solve for x.
-0.5x^2 + 40x - 300 = 15,000
-0.5x^2 + 40x - 15,300 = 0

Added by Jessica K.

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