Advertisements
Advertisements
Question
A from produces two types of calculates each week, x number of type A and y number of type B. The weekly revenue and cost functions = (in rupees) are R(x, y) = 80x + 90y + 0.04xy – 0.05x2 – 0.05y2 and C(x, y) = 8x + 6y + 2000 respectively. Find `(del"P")/(delx)` (1200, 1800) and `(del"P")/(dely)` (1200, 1800) and interpret these results
Advertisements
Solution
`(del"P")/(delx)` = 72 + 0.04y – 0.1x
`(del"P")/(delx)` (1200, 1800) = 72 + 0.04 × 1800 – 0.1 × 1200
= 72 + 72 – 120
= 144 – 120
= 24
`(del"P")/(dely)` = 84 + 0.04x – 0.1y
`(del"P")/(dely)` (1200, 1800) = 84 + 0.04 × 1200 – 0.1 × 1800
= 84 + 48 – 180
= 132 – 180
= – 48
APPEARS IN
RELATED QUESTIONS
If z = (ax + b) (cy + d), then find `(∂z)/(∂x)` and `(∂z)/(∂y)`.
If u = exy, then show that `(del^2"u")/(delx^2) + (del^2"u")/(del"y"^2)` = u(x2 + y2).
If u = 4x2 + 4xy + y2 + 4x + 32y + 16, then `(del^2"u")/(del"y" del"x")` is equal to:
If u = x3 + 3xy2 + y3 then `(del^2"u")/(del "y" del x)`is:
If u = `e^(x^2)` then `(del"u")/(delx)` is equal to:
Find the partial dervatives of the following functions at indicated points.
f(x, y) = 3x2 – 2xy + y2 + 5x + 2, (2, – 5)
For the following functions find the fx, and fy and show that fxy = fyx
f(x, y) = `(3x)/(y + sinx)`
If U(x, y, z) = `(x^2 + y^2)/(xy) + 3z^2y`, find `(del"U")/(delx), (del"U")/(dely)` and `(del"U")/(del"z)`
For the following functions find the gxy, gxx, gyy and gyx
g(x, y) = log(5x + 3y)
Let w(x, y, z) = `1/sqrt(x^2 + y^2 + z^2)` = 1, (x, y, z) ≠ (0, 0, 0), show that `(del^2w)/(delx^2) + (del^2w)/(dely^2) + (del^2w)/(delz^2)` = 0
If V(x, y) = ex (x cosy – y siny), then Prove that `(del^2"V")/(delx^2) + (del^2"V")/(dely^2)` = 0
If w(x, y) = xy + sin(xy), then Prove that `(del^2w)/(delydelx) = (del^2w)/(delxdely)`
If v(x, y) = `x^2 - xy + 1/4 y^2 + 7, x, y ∈ "R"`, find the differential dv
Let V (x, y, z) = xy + yz + zx, x, y, z ∈ R. Find the differential dV
Choose the correct alternative:
If g(x, y) = 3x2 – 5y + 2y2, x(t) = et and y(t) = cos t then `"dg"/"dt"` is equal to
