# Thread: Help me with linear programming

1. ## Help me with linear programming

SOLVE THE LINEAR PROGRAMMING SITUATION:

The bakery is making bread and muffins. (Use b for bread and m for muffins)

The bread takes 4 hours to prepare and 1 hour to bake.
The muffins take .5 hours to prepare and .5 hours to bake.
The maximum preparation time available is 16 hours.
The maximum baking time available is 10 hours.

For each batch of bread the make $35 profit. For each batch of muffins they make$10 profit.

How many batches of bread and muffins should be made to maximize profit?

I need the system of inequalities, the vertices, the maximizing equation, all work shown, a graph, and the solution.

2. Hi there brittanielane, welcome to the forum.

Let's look at the problem as follows, you have 2 items and each need preparation and baking.

Let's call the numbers (loaves) of bread = B and the number of muffins made = M

Now for preparation and baking you need to come up with a separate equation in terms of B and M. These will be your contraints.

Here's a hint.

Preparation: $\displaystyle \dots + \dots \leq 16$

Baking: $\displaystyle \dots + \dots \leq 10$

The objective function in this case will maximise profit, let's call that P, is also in terms of B and M.

3. The "fundamental theorem" of linear programming is: "the max or min of a linear function, on a convex polygon, occurs at one of the vertices". Determine the lines that bound the "feasible region", determine the vertices at which they cross, and evaluate the object function at each vertex to see where it has maximum value.