Suppose you are in charge of selling n types of products in your company. In particular,

must decide the sale price and the quantity to offer to the market of each of the products in

the set {1, ..., n} (you can assume that these products are divisible). A market study

has determined that the price per unit (p j ) and demand q j (in units demanded) of a

Product j are related by the equation q j = h j p j , where h j > 0 is a known parameter.

Additionally, for logistical reasons, he knows that he cannot sell beyond U> 0 units in total

adding all the products offered.

(i) Formulate a nonlinear optimization model that allows finding the price and quantity

optimal to sell for each of the products in order to maximize total income.

(ii) Show that the formulated problem admits an optimal solution