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Trady 14. The profit function for one acre of soybeans is: P(x,y) = .01(-x + 3xy...
14. The profit function for one acre of soybeans is: P(x, y) =.01(-x² + 3xy +160x...
14. The profit function for one acre of soybeans is: P(x, y) =.01(-x² + 3xy +160x - 5y2 + 200 y + 2600) where x is the unit cost of fertilizer and y is the unit cost of hybrid soybean seed. Hint: Use partial derivatives to set-up a system of equations to solve to find maximum values. a) Find x and y values that maximize profit. b) Find the value of maximum profit.
5. Suppose that a firm's total profit function is P(x,y) = 2xy + 2y+12-(2x2 +y2), where...
5. Suppose that a firm's total profit function is P(x,y) = 2xy + 2y+12-(2x2 +y2), where x is amount of production and sales of the first product and y - of the second produc 1) Find all first and second order partial derivatives. 2) Find values of x and y that maximize the profit. Find the maximum profit. 6. Ifx thousand euros is spend on labor and y thousand euros is spend on equipment, the outpu certain factory will be...
#10 and #12 8. Find all points (.y) where fCx.y) -3x2 + 7xy -4y2 + x + y has possible relative maximum or minimum values 9. Find all points (x,y, z) where f(x,y,z) 5+ 8x 4y+x2+y2 z2has possibl...
#10 and #12
8. Find all points (.y) where fCx.y) -3x2 + 7xy -4y2 + x + y has possible relative maximum or minimum values 9. Find all points (x,y, z) where f(x,y,z) 5+ 8x 4y+x2+y2 z2has possible relativema imun or minimum value 10. Both first partial derivatives of f(x.y)-x-4xyy are zero at the points (0 11. Find all points (x,y) where f(e.y) 2x2+3xy + 5y has possible relative maximum or minimum values. Then, use the 12. Use the second...
A firm’s demand function is p=60-0.5Q If fixed cost are 10 and variable cost are Q+3...
A firm’s demand function is p=60-0.5Q If fixed cost are 10 and variable cost are Q+3 per unit, find the maximum profit. Q2. Which of the following could represent a function, f(x,y), with first-order partial derivatives af/ax = 3xy(xy+2) af/ay=x^2(2xy+3) Q3. Find the value of dy/dx at the point (-2,1) for the function which is defined implicitly by x^2 - x/y =6 Q4. Find the value of the marginal rate of technical substitution for the production function Q=300 (K^2/3 )(L^1/2)...
4. The demands for a monopolist's two products are determined by the equations p=25 - x and q=24 - 2y, where p and q ar...
4. The demands for a monopolist's two products are determined by the equations p=25 - x and q=24 - 2y, where p and q are prices per unit of the two goods, and x and y are the corresponding quantities. The costs of producing x units of the first good and y units of the other are C(x,y) = 3x + 3xy + y2 (a) Find the monopolist's profit (x,y) from producing and selling x units of the first good...
6. The profit function of a firm is (x,y) = px +qy-ar? - By?, where p...
6. The profit function of a firm is (x,y) = px +qy-ar? - By?, where p and q are the prices per unit and ar? + By are the costs of producing and selling x units of the first good and y units of the other. The constants are all positive. (a) Find the values of x and y that maximize profits. Denote them by x* and y'. Verify that the second-order conditions are satisfied. (1) Define (p, q) =...
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 x is the amount spent on advertising, in P(x,y)= 4xy +50y - 9y? 10 1 y-80 Find the values of x and y that maximize the profit function, the maximized function value, and interpret these results. The maximum function value occurs at POD-1 The maximum profit of $is attained when is spent on advertising and the company charges per item...
3. A monopolist sells two products x and y for which the demand functions are P....
3. A monopolist sells two products x and y for which the demand functions are P. 84-4x, P. = 127-3y, and the combined total cost function is TC = 2x² + 3xy +4 y2 +64. a. Find the profit function. b. Find the profit-maximizing level of output for each product. c. Find the profit-maximizing price for each product. d. Find the maximum profit.
How to solve #7 Suppose that /(x,y)=(x+y2)3. Find s. and at the port az) , supportait atturbanco nennt.yoy, tindhaw.th.he%.anda 7. in a certain suburban community, commuters have the choice of geting...
How to solve #7
Suppose that /(x,y)=(x+y2)3. Find s. and at the port az) , supportait atturbanco nennt.yoy, tindhaw.th.he%.anda 7. in a certain suburban community, commuters have the choice of geting into the ity by bus or train. The demand for these modes of transportation variles with their cost Let /(P.,P) be the number of people who will take the train when p, i the price of the bus ride and py is the price of the train ride. Would...
у 1200- A firm has the marginal profit function below, where P(x) is the profit earned...
у 1200- A firm has the marginal profit function below, where P(x) is the profit earned at x dollars per unit. dP 9000 - 3000x dx (x2 - 6x+ (+10) 2 600- 0- LY 6 8 -600- The graph of this function is shown to the right. Find the total-profit function given that P = $1500 at x = $3. -1200- How can the total-profit function be found? A. Substitute the given value of P into the marginal-profit function and...
14. The profit function for one acre of soybeans is: P(x, y) =.01(-x² + 3xy +160x - 5y2 + 200 y + 2600) where x is the unit cost of fertilizer and y is the unit cost of hybrid soybean seed. Hint: Use partial derivatives to set-up a system of equations to solve to find maximum values. a) Find x and y values that maximize profit. b) Find the value of maximum profit.
5. Suppose that a firm's total profit function is P(x,y) = 2xy + 2y+12-(2x2 +y2), where x is amount of production and sales of the first product and y - of the second produc 1) Find all first and second order partial derivatives. 2) Find values of x and y that maximize the profit. Find the maximum profit. 6. Ifx thousand euros is spend on labor and y thousand euros is spend on equipment, the outpu certain factory will be...
#10 and #12
8. Find all points (.y) where fCx.y) -3x2 + 7xy -4y2 + x + y has possible relative maximum or minimum values 9. Find all points (x,y, z) where f(x,y,z) 5+ 8x 4y+x2+y2 z2has possible relativema imun or minimum value 10. Both first partial derivatives of f(x.y)-x-4xyy are zero at the points (0 11. Find all points (x,y) where f(e.y) 2x2+3xy + 5y has possible relative maximum or minimum values. Then, use the 12. Use the second...
4. The demands for a monopolist's two products are determined by the equations p=25 - x and q=24 - 2y, where p and q are prices per unit of the two goods, and x and y are the corresponding quantities. The costs of producing x units of the first good and y units of the other are C(x,y) = 3x + 3xy + y2 (a) Find the monopolist's profit (x,y) from producing and selling x units of the first good...
6. The profit function of a firm is (x,y) = px +qy-ar? - By?, where p and q are the prices per unit and ar? + By are the costs of producing and selling x units of the first good and y units of the other. The constants are all positive. (a) Find the values of x and y that maximize profits. Denote them by x* and y'. Verify that the second-order conditions are satisfied. (1) Define (p, q) =...
A one product company finds that its profit. P. in millions of dollars, is given by the following equation where x is the amount spent on advertising, in P(x,y)= 4xy +50y - 9y? 10 1 y-80 Find the values of x and y that maximize the profit function, the maximized function value, and interpret these results. The maximum function value occurs at POD-1 The maximum profit of $is attained when is spent on advertising and the company charges per item...
3. A monopolist sells two products x and y for which the demand functions are P. 84-4x, P. = 127-3y, and the combined total cost function is TC = 2x² + 3xy +4 y2 +64. a. Find the profit function. b. Find the profit-maximizing level of output for each product. c. Find the profit-maximizing price for each product. d. Find the maximum profit.
How to solve #7
Suppose that /(x,y)=(x+y2)3. Find s. and at the port az) , supportait atturbanco nennt.yoy, tindhaw.th.he%.anda 7. in a certain suburban community, commuters have the choice of geting into the ity by bus or train. The demand for these modes of transportation variles with their cost Let /(P.,P) be the number of people who will take the train when p, i the price of the bus ride and py is the price of the train ride. Would...
у 1200- A firm has the marginal profit function below, where P(x) is the profit earned at x dollars per unit. dP 9000 - 3000x dx (x2 - 6x+ (+10) 2 600- 0- LY 6 8 -600- The graph of this function is shown to the right. Find the total-profit function given that P = $1500 at x = $3. -1200- How can the total-profit function be found? A. Substitute the given value of P into the marginal-profit function and...
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