Interrelated Product Optimization

We were given this today in class and told to complete it. I am still confused by it.

" A company produces and sells three interrelated products w, x, and y. They need to determine the optimum weekly production of each, ie w units of W, x units of X, y units of Y. However, the price demand function for the each of the products are linked together as follows:

Price of W = 40 -0.2w +0.1x +0.2y

Price of X= 60 +0.1w -0.15x +0.05y

Price of Y= 60 +0.05w +0.05x - 0.25y

The total weekly cost of producing w,x, and y units of the three products is given by:

Total weekly cost = 5000 +10w +20x +10y

A) From the price demand functions for W,X, and Y find the weekly revenues from the sales of each product in terms of w,x and y.

B) Write down the total weekly revenue and the total weekly profit from the combined sales of W, X and Y

C) Write down all the relevant partial derivatives of total weekly profit.

D) Find the optimum mix of production of W,X and Y that maximises the weekly profit.