Solve for the following linear programming problem graphically:

Lesson 6. Linear Programming 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. Maximize: Z = 5x + 3y subject to 3x + 5y 15, 5x + 2y 10, x 0, y 0

2. Minimize: Z = x + 2y subject to 2x + y 3, x + 2y 6, x 0, y 0 3. The Chiffon cake requires 200 g of flour and 25 g of fat, and the Banana cake requires 100 g of flour and 50 g of fat.

3.Find the maximum number of Chiffon and Banana Cakes which can be made from 5 kg (5000 g) of flour and 1 kg (1000 g) of fat assuming that there is no shortage of the other ingredients used in making the cakes.