Let P(x,y) = -15x^2 -2y^2 + 10xy + 10x +8y + 11 where P(x,y) is the...

Let P(x,y) = -15x^2 -2y^2 + 10xy + 10x +8y + 11 where P(x,y) is the profit in dollars when x hundred unit of item A and y hundred units of item B are produced and sold.

A.Find how many items of each type should be produced to maximize profit?

B.Use the Second Derivates Test for local extrema to show that this number of items A and B results in a maximum?

Expert Solution

milcah answered 2 years ago

1) x2y'' - 8xy' - 8y =0 2) y''- 3y' - 2y = 10sin(x)

Maximize p = x + 8y subject to x + y ≤ 25 y ≥ 10...

Maximize p = x + 8y subject to x + y ≤ 25 y ≥ 10 2x − y ≥ 0 x ≥ 0, y ≥ 0. P=? (X,Y)= ? (NOT BY GRAPHING)

Let f(x,y) = 3x3 + 3x2 y − y3 − 15x. a) Find and classify the...

Let f(x,y) = 3x3 + 3x2 y − y3 − 15x. a) Find and classify the critical points of f. Use any method taught during the course (the second-derivative test or completing the square). b) One of the critical points is (a,b) = (1,1). Write down the second-degree Taylor approximation of f about this point and motivate, both with computations and with words, how one can see from this approximation what kind of critical point (1,1) is. Use completing the...

Let f(x,y) = 3x3 + 3x2 y − y3 − 15x. a) Find and classify the...

Let f(x,y) = 3x3 + 3x2 y − y3 − 15x. a) Find and classify the critical points of f. Use any method taught during the course (the second-derivative test or completing the square). b) One of the critical points is (a,b) = (1,1). Write down the second-degree Taylor approximation of f about this point and motivate, both with computations and with words, how one can see from this approximation what kind of critical point (1,1) is. Use completing the...

Let f(x, y) = xy3 − x 2 + 2y − 1. (a) Find the gradient...

Let f(x, y) = xy3 − x 2 + 2y − 1. (a) Find the gradient vector of f(x, y) at the point (2, 1). (b) Find the directional derivative of f(x, y) at the point (2, 1) in the direction of ~u = 1 √ 10 (3i + j). (c) Find the directional derivative of f(x, y) at point (2, 1) in the direction of ~v = 3i + 2j.

Let f(x, y) = 5x 2y − 3x2 + 2y3 + 3xy, P be the point (1,...

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Maximize p = 13x + 8y subject to x + y ≤ 25 x ≥ 10...

Maximize p = 13x + 8y subject to x + y ≤ 25 x ≥ 10 −x + 2y ≥ 0 x ≥ 0, y ≥ 0. P = ? (X,Y)= ( ?,? )

y"-2y'+2y = x^2+e^2x

y"-8y'+20y = (13x^2+x)e^x

Consider the following utility function: U(x, y) = 10x + 2y. A consumer faces prices of...

Consider the following utility function: U(x, y) = 10x + 2y. A consumer faces prices of px = 1 and py = 2. Assuming that graphically good x is on the horizontal axis and good y is on the vertical axis, suppose the consumer chooses to consume 5 units of good x and 13 units of good y. What is the marginal rate of substitution (MRS) equal to?

Question

Let P(x,y) = -15x^2 -2y^2 + 10xy + 10x +8y + 11 where P(x,y) is the...

Solutions

Expert Solution

Related Solutions

1) x2y'' - 8xy' - 8y =0 2) y''- 3y' - 2y = 10sin(x)

Maximize p = x + 8y subject to x + y ≤ 25 y ≥ 10...

Let f(x,y) = 3x3 + 3x2 y − y3 − 15x. a) Find and classify the...

Let f(x,y) = 3x3 + 3x2 y − y3 − 15x. a) Find and classify the...

Let f(x, y) = xy3 − x 2 + 2y − 1. (a) Find the gradient...

Let f(x, y) = 5x 2y − 3x2 + 2y3 + 3xy, P be the point (1,...

Maximize p = 13x + 8y subject to x + y ≤ 25 x ≥ 10...

y"-2y'+2y = x^2+e^2x

y"-8y'+20y = (13x^2+x)e^x

Consider the following utility function: U(x, y) = 10x + 2y. A consumer faces prices of...