a company's revenue function is given by - q³+370q² and its cost function is given 380 + 12q, where q is hundreds of units sold/produced, while R(q) and C(q) are in total dollars of revenue and cost, respectively. Suppose R(q) by C(q) = = A) Find a simplified expression for the marginal profit function. (Be sure to use the proper variable in your answer.)

Consider the following cost function: 3 C=0.2q³-6q² + 80q + 150. (Enter a numeric response using a real number rounded to two decimal places.) When output is 19 units, average cost is $ When output is 19 units, marginal cost is $ The output level where average variable cost equals marginal cost is units.

The marginal revenue (in thousands of dollars) from the sale of x handheld gaming devices is given by the following function. R'(x) = 4x (x²+25,000) (a) Find the total revenue function if the revenue from 120 devices is $34,166. (b) How many devices must be sold for a revenue of at least $50,000? (a) The total revenue function is R(x), given that the revenue from 120 devices is $34,166. (Round to the nearest integer as needed.) (b) devices must be sold to generate a revenue of at least $50,000 (Type a whole number.)

Consider the following total revenue function for a hammer. R 44x 0.01x2 (a) The sale of how many hammers, x, will maximize the total revenue in dollars? x = 2200 hammers Find the maximum revenue. $48400 (b) Find the maximum revenue if production is limited to at most 1200 hammers. $ If the total revenue function for a computer is R(x) = 1000x - 35x2-x³, find the level of sales, x, that maximizes revenue and find the maximum revenue in dollars. x = R(x) = $ computers If the total cost function for producing x lamps is C(x) = 3240 + 37x+ 0.9x2 dollars, producing how many units, x, will result in a minimum average cost per unit? units Find the minimum average cost per unit. $ If the total cost function for a product is C(x) = 10+ 0.1x2 dollars, producing how many units, x, will result in a minimum average cost per unit? x= units Find the minimum average cost per unit. $ Find the derivative of the function. f(x) = ex-xe