Given cost and price​ (demand) functions C(q)=110q+43,000 and p(q)=−1.9q+880​, what price maximizes​ revenue?   It would be ​$enter your response here   per item. ​(Round answer to two decimal​ places.)

How can you use the discriminant when you are graphing a quadratic function?

At the Pizza Dude restaurant, a 12-in. pizza costs 5.40 to make, and the manager wants to make at least 4.80 from the sale of each pizza. If the pizza will be sold by the slice and each pizza is cut into 6 pieces, what is the minimum charge per slice?

If you perform your break-even analysis and there is more than one solution, explain how you would determine which x-values are profit and which are not.

Find the break-even point when the cost function is   C=$20x+$3,235   and the revenue function is  R=$293x, where   ?x    is the number of the units of the product or service produced and sold. (Round your final answer to the nearest whole digit).

Do the following

The total revenue function for a product is given by R = 540x dollars, and the total cost function for this same product is given by C = 13,500+ 60x + x², where C is measured in dollars. For both functions, the input x is the number of units produced and sold. a. Form the profit function for this product from the two given functions. b. What is the profit when 24 units are produced and sold? c. What is the profit when 38 units are produced and sold? d. How many units must be sold to break even on this product? (・・・))) a. Write the profit function. P(x) = (Simplify your answer.) b. When 24 units are produced and sold, there is a of $. (Simplify your answer.) c. When 38 units are produced and sold, there is of $. a (Simplify your answer.) d. The number of units that must be sold to break even on this product is. (Simplify your answer. Use a comma to separate answers as needed.)

Please provide in clear and complete step-by-step solutions in scanned handwriting or computerized output

For a manufacturer's product, the demand function is p= 240 + 57q- q At what level of output (value of q ) does the revenue function change from increasing to decreasing behavior?