Question

For a certain company, the cost for producing x items is 50x+300 and the revenue for selling x items is 90x−0.5x^2.

Part a: Set up an expression for the profit from producing and selling x items.

Part b: Find two values of x that will create a profit of $50.

What does x equal?

Part c: Is it possible for the company to make a profit of $2,500?

Answer 1

Profit is the difference between revenue and cost, expressed as the equation Profit = (90x - 0.5x^2) - (50x + 300). To find x for a $50 profit, solve the quadratic equation obtained by setting the profit to 50. To determine if a $2,500 profit is possible, solve for x by setting profit to 2,500 in the same profit equation.

Step-by-step explanation:

For Part a, the profit from producing and selling x items can be calculated as the difference between total revenue and total costs, which is expressed as:

Profit = Revenue - Cost = (90x - 0.5x^2) - (50x + 300).

For Part b, to find values of x that generate a $50 profit, set the profit equation equal to 50 and solve for x:

50 = (90x - 0.5x^2) - (50x + 300).

After simplifying, you will obtain a quadratic equation and use the quadratic formula to find two values for x.

For Part c, to check if it's possible for the company to make a profit of $2,500, set the profit equation to 2,500:

2,500 = (90x - 0.5x^2) - (50x + 300).

Again, solving this quadratic equation will show if such an x value exists.