Linear Programming is the topic.

One of the goals of this course is to learn how to manage limited resources without sacrificing a certain target. Linear Programming is a mathematical method of finding the best solution to a certain objective subject to a given set of constraints. In business, linear programming is finding the optimal solution to a certain objective function (maximizing profit or minimizing cost)given scarce resources (constraints). These constraints are expressed as linear inequalities while the objective function is a linear function.

1. Shade the region representing the solution set (area of feasible solution) of the following set of inequalities.(recall graphing of inequalities in two variables) 3x + y 6, 4x + 3y 12, x 0, and y 0. 2. Minimize the objective function z = 10x+ 9y subject to the constraints 3x+y 6, 4x+ 3y 12, x 0, and y 0.

1. Maximize the objective function z = 8x + 10y subject to the constraints 3x + 5y 15, 5x + 2y 10, x 0, and y 0. 2. Danilo wishes to mix two types of food C and D in such a way that the vitamin contents of the mixture contain at least 8 units of vitamin A and 11 units of Vitamin B. Food C costs Php 54/kg and Food D costs Php 72/kg. Food C contains 3 units /kg of vitamin A and 5 units /kg of Vitamin B while Food D contains 4 units /kg of vitamin A and 2 units /kg of vitamin B. What is the objective function?