A one product company finds that its profit. P. in millions of dollars, is given by...
A one-product company finds that its profit, P, in millions of dollars, is given by the following equation where a is the amount spent on advertising, in millions of dollars, and p is the price charged per item of the product, in dollars. P(a.p)= 2ap + 80p – 15p? - Hoa?p-120 Find the maximum value of P and the values of a and p at which it is attained. The maximum value of P is attained when a is $1...
The profit p(x) of a cosmetics company , in thousands of dollars,is given by p(x)=-5x^2+400x-2550, where x is the amount spent on advertising , in thousands of dollarsa) determine the max profit the company can makeb)Determine the amount spent on advertising that will result in the max profitc)What amount must be spent on advertising to obtain a profit of at least $4 000 000
Problem 1: An ice cream shop finds that its weekly profit P (measured in dollars) as a function of the price x (measured in dollars) it charges per ice cream cone is given by the function k, defined by kx)-125x2 +670x 125 where P k(x). a) Determine the maximum weekly profit and the price of an ice cream cone that produces that maximum profit b) The cost of the ice cream cone is too low then the ice cream shop...
The monthly profit from the sale of a product is given by P = 18x − 0.1x2 − 100 dollars. (a) What level of production maximizes profit? (b) What is the maximum possible profit?
5. Suppose that the demand equation for a monopolist's product is p = 400 - 2q and the average cost function is c = 0.29 + 4 + toº, where q is number of units, and both p and c are expressed in dollars per unit. a) Determine the level of output at which profit is maximized b) Determine the price at which maximum profit occurs c) Determine the maximum profit d) If, as a regulatory device, the government imposes...
Sheet A company produces units of product and units of product (both in hundreds per month). The monthly profit equation (in thousands of dollars) is given by the following: P(x,y) - 4x2 + 4xy - 3y2 + 4x + 10y + 81 Find and evaluate . Use formulas to get an exact answer! Pxx.y) Px(1,3) What does this value mean? Answer in this textbox. Answer: What is the critical point of? What are the equations for, and ? o po...
Sheet A company produces units of product and units of product (both in hundreds per month). The monthly profit equation (in thousands of dollars) is given by the following: P(x,y) - 4x2 + 4xy - 3y2 + 4x + 10y + 81 Find and evaluate . Use formulas to get an exact answer! Pxx.y) Px(1,3) What does this value mean? Answer in this textbox. Answer: What is the critical point of? What are the equations for, and ? o po...
Listed below are paired data consisting of amounts spent on advertising (in millions of dollars) and the profits (in millions of dollars). Determine if there is a significant positive linear correlation between advertising cost and profit. Use a significance level of 0.06 and round all values to 4 decimal places. Advertising Cost Profit 3 17 4 24 5 25 6 18 7 29 8 23 9 28 10 34 11 35 R vector x values: 3,4,5,6,7,8,9,10,11 R vector y values:...
A company manufactures two products. The price function for product A is p = 19 − 1 2 x (for 0 ≤ x ≤ 38), and for product B is q = 33 − y (for 0 ≤ y ≤ 33), both in thousands of dollars, where x and y are the amounts of products A and B, respectively. If the cost function is C(x, y) = 11x + 17y − xy + 7 thousands of dollars, find the quantities...
A particular computing company finds that its weekly profit, in dollars, from the production and sale of x laptop computers is P(x) = -0.003x -0.2x + 600x - 800 Currently the company builds and sells 8 laptops weekly a) What is the current weekly profit? b) How much profit would be lost if production and sales dropped to 7 laptops weekly? c) What is the marginal profit when x = 8? d) Use the answer from part (a) and (c)...