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3) Suppose that the price p (in dollars) and weekly sales x (in 1000s) of light bulbs satisfy the demand equation 2...
Suppose that the price p, in dollars, and the weekly sales x, in dozens of units,...
Suppose that the price p, in dollars, and the weekly sales x, in dozens of units, of a certain cannabis commodity satisfy the demand equation 6p3 + 2x2 = 234. Determine the rate at which sales are changing at a time when x = 6, p = 3, and the price is increasing at $.25 per week. Be clear in your answer as to whether sales are rising or falling.
A company manufactures and sells x cellphones per week. The weekly price-demand and cost equation...
#4
& 5, work shown.
A company manufactures and sells x cellphones per week. The weekly price-demand and cost equations are given below. 4) p 400-0.lx and C(x)-25,000+135x Find the weekly revenue function. What price should the company charge for the phones, and how many phones should be produced to maximize the weekly revenue? What is the weekly revenue? a) b) c) Find the weekly profit function. What price should the company charge for the phones, and how many phones...
Suppose that the supply of x units of a product at price p dollars per unit...
Suppose that the supply of x units of a product at price p dollars per unit is given by the following. p = 30 + 60 In(8x + 2) (a) Find the rate of change of supply price with respect to the number of units supplied. dp dx = (b) Find the rate of change of supply price when the number of units is 31. $ (c) Approximate the price increase associated with the number of units supplied changing from...
4.) Suppose the demand D and unit price p of a particular baseball player's jerseys are...
4.) Suppose the demand D and unit price p of a particular baseball player's jerseys are related by the exponential demand function D = 7500e -0.001p, a.) Find the unit price that maximizes revenue. b.) What is the maximum revenue that can be earned when selling these jerseys? T(t) 5.) The total number of online orders a company receives is given by 15 1 + 250-0.5 thousand orders t weeks after the website began advertising. Use your calculator to graph...
Find the equation of the tangent line to the curve when x has the given value....
Find the equation of the tangent line to the curve when x has the given value. 7) f(x) = 4,x=5 8) f(x) = }x=3 11) Solve the problem. 11) The profit in dollars from the sale of thousand compact disc players is P(x) = x3 - 5x2 + 3x + 8. Find the marginal profit when the value of x is 6. 12) 12) Ir the price of a product is given by Px) E 1200, where x represents the...
15. Suppose demand, D, for a good is a linear function of its price per unit,...
15. Suppose demand, D, for a good is a linear function of its price per unit, P. When price is $20, demand 16. A certain firm posted an ad for a sales representative position paying S36,000 base salary plus a. What commission rate (as a percent of sales) must he earn to make $63,000 per year? is 100 units, and when price is $10, demand is 150 units. Find the demand function. commission. Based on his past experience, a salesman...
c) The demand function for books in Pick n Pay is given by P quantity demanded and P is the price per book. 50-0.3Q, where Q is the i. Find the number of books that will be bought when the price is K...
c) The demand function for books in Pick n Pay is given by P quantity demanded and P is the price per book. 50-0.3Q, where Q is the i. Find the number of books that will be bought when the price is K2. ii. iii. Find the price elasticity of the demand when the number of books bought is 30. ] Calculate the percentage change in quantity demanded when the price increases by 10% (use the coefficient price elasticity of...
Because the derivative of a function represents both the slope of the tangent to the curve...
Because the derivative of a function represents both the slope of the tangent to the curve and the instantaneous rate of change of the function, it is possible to use information about one to gain information about the other. Consider the graph of the function y = f(x) given in the figure. (a) Over what interval(s) (a) through (d) is the rate of change of f(x) positive? (Select all that apply.) OOOO (b) Over what interval(s) (a) through (d) is...
2.If C(x) is the cost of producing x units of a commodity, then the average cost...
2.If C(x) is the cost of producing x units of a commodity, then the average cost per unit is c(x) = C(x)/x. Consider the cost function C(x) given below. C(x) = 24,000 + 290x + 6x3/2 (a) Find the total cost at a production level of 1000 units. (Round your answer to the nearest cent.) $ (b) Find the average cost at a production level of 1000 units. (Round your answer to the nearest cent.) $ per unit (c) Find...
2-6% each part Suppose we have opened a catfish hot dog stand at the mall which will be open 4 hours per day. We are test marketing our sales at various prices to attempt to determine the best p...
2-6% each part Suppose we have opened a catfish hot dog stand at the mall which will be open 4 hours per day. We are test marketing our sales at various prices to attempt to determine the best price we should use for our catfish hot dogs. So, let: Price of the Number of y hot dogs $1.50 $3.00 $4.00 hot dogs sold 182 118 39 Notice that we have put these variables in the same order that we did...
Suppose that the price p, in dollars, and the weekly sales x, in dozens of units, of a certain cannabis commodity satisfy the demand equation 6p3 + 2x2 = 234. Determine the rate at which sales are changing at a time when x = 6, p = 3, and the price is increasing at $.25 per week. Be clear in your answer as to whether sales are rising or falling.
#4
& 5, work shown.
A company manufactures and sells x cellphones per week. The weekly price-demand and cost equations are given below. 4) p 400-0.lx and C(x)-25,000+135x Find the weekly revenue function. What price should the company charge for the phones, and how many phones should be produced to maximize the weekly revenue? What is the weekly revenue? a) b) c) Find the weekly profit function. What price should the company charge for the phones, and how many phones...
Suppose that the supply of x units of a product at price p dollars per unit is given by the following. p = 30 + 60 In(8x + 2) (a) Find the rate of change of supply price with respect to the number of units supplied. dp dx = (b) Find the rate of change of supply price when the number of units is 31. $ (c) Approximate the price increase associated with the number of units supplied changing from...
4.) Suppose the demand D and unit price p of a particular baseball player's jerseys are related by the exponential demand function D = 7500e -0.001p, a.) Find the unit price that maximizes revenue. b.) What is the maximum revenue that can be earned when selling these jerseys? T(t) 5.) The total number of online orders a company receives is given by 15 1 + 250-0.5 thousand orders t weeks after the website began advertising. Use your calculator to graph...
Find the equation of the tangent line to the curve when x has the given value. 7) f(x) = 4,x=5 8) f(x) = }x=3 11) Solve the problem. 11) The profit in dollars from the sale of thousand compact disc players is P(x) = x3 - 5x2 + 3x + 8. Find the marginal profit when the value of x is 6. 12) 12) Ir the price of a product is given by Px) E 1200, where x represents the...
15. Suppose demand, D, for a good is a linear function of its price per unit, P. When price is $20, demand 16. A certain firm posted an ad for a sales representative position paying S36,000 base salary plus a. What commission rate (as a percent of sales) must he earn to make $63,000 per year? is 100 units, and when price is $10, demand is 150 units. Find the demand function. commission. Based on his past experience, a salesman...
c) The demand function for books in Pick n Pay is given by P quantity demanded and P is the price per book. 50-0.3Q, where Q is the i. Find the number of books that will be bought when the price is K2. ii. iii. Find the price elasticity of the demand when the number of books bought is 30. ] Calculate the percentage change in quantity demanded when the price increases by 10% (use the coefficient price elasticity of...
Because the derivative of a function represents both the slope of the tangent to the curve and the instantaneous rate of change of the function, it is possible to use information about one to gain information about the other. Consider the graph of the function y = f(x) given in the figure. (a) Over what interval(s) (a) through (d) is the rate of change of f(x) positive? (Select all that apply.) OOOO (b) Over what interval(s) (a) through (d) is...
2-6% each part Suppose we have opened a catfish hot dog stand at the mall which will be open 4 hours per day. We are test marketing our sales at various prices to attempt to determine the best price we should use for our catfish hot dogs. So, let: Price of the Number of y hot dogs $1.50 $3.00 $4.00 hot dogs sold 182 118 39 Notice that we have put these variables in the same order that we did...
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