A Chemist produces two new types of fertilizers x and y. The profits realized from a kilo of Type x is P50 and from a kilo of Type y is P75. The raw materials from which the fertilizers are made are...

A Chemist produces two new types of fertilizers x and y. The profits realized from a kilo of Type x is P50 and from a kilo of Type y is P75. The raw materials from which the fertilizers are made are nitrogen sulfur and potassium which are used in the following quantities:

Nitrogen Sulfur

Potassium

x 4 Kilos 4 Kilos 9 Kilos

y 3 Kilos 2 Kilos 1 Kilos

The available stocks include 1,500 kilos of nitrogen, 1,200 kilos of potassium and 1,200 kilos of sulfur. Find the amounts of x and y to be produced in order to maximize the profit.

Required:

1) Develop the Linear Programming Model

2) Identify the optimum number of x and y to be produced to maximize the profit using the graphical method.