Answer to Question #203693 in Economics for Muhammad Humayun

Question

Q2) Sales are a function of advertising in newspapers and magazines (X, Y).              10

S = 100X^0.5 Y^0.5

Price of advertising in newspapers and magazines are Rs.30 and Rs.40 respectively. The total budget for advertising is Rs.1200. For maximizing the sales, find out the best combination of advertisement in newspapers and magazines by using lagrangian multiplier

Answer 1

$$f(x,y)=100x^{0.5}y^{0.5}-\lambda(30x+40y-1200)$$

$$\frac{\delta f}{\delta x}=50(\frac{y}{x})^{0.5}-30\lambda$$

$$\frac{\delta f}{\delta y}=50(\frac{x}{y})^{0.5}-40\lambda$$

$$y=0.75x$$

$$x=20$$

$$y=15$$