Sec. 3.3 In each of the following linear programming problems, do the following: а. Define variables. b. Determine constraints. Determine objective function. d. Graph the feasible region. Find the corner points. С. е. f. Evaluate the objective function at each corner point. Write the conclusion to the problem. g. 1. A bakery makes two types of cakes each day: poppy seed and German chocolate. The profit to the bakery is $3 on each poppy seed cake and $4.50 on each German chocolate cake. A poppy seed cake requires 400 grams of flour, 200 grams of butter, and 100 grams of poppy seeds. A German chocolate cake requires 600 grams of flour, 100 grams of butter, and 140 grams of chocolate. There are 10,200 grams of flour, 2,500 grams of butter, 1,200 grams of poppy seeds, and 2,100 grams of chocolate. How many cakes of each type should be made to yield maximum profit? How much profit is made?

A mathematical statement, which states that two expressions are not equal is called an inequation and is denoted by $x\ne y$.

A mathematical statement, which states that one expression is greater than the other in value is called an inequality.

The mathematical problems where we have to either maximize or minimize a linear function $Z=ax+by$ constrained by certain conditions in the form of linear inequalities are called Linear Programming problems.

Here a and b are constants and x and y are variables and the linear function is called the objective function. There are several methods to find the optimum solution for the objective function. Mostly we use the graphical method.

In the graphical method, we first find the critical points(corner points) and then substitute those points in the objective function to obtain the optimum solution.