Context 11 - Hopping Toward Optimization

Read the scenario above.

How will you know when you have answered this question? What do you need to state in your answer?

Select variables for the two values you are trying to find to answer this question. (Don’t forget to write what your variables represents.)

What do we want to maximize? Write an expression for what we want to maximize.

The max or min amounts lead to constraints on how many mugs and bowls can be made. We write these constraints as inequalities.

Write an inequality using the fact that only 15 boxes are available for shipping.

Write an inequality indicating there are 24 hours available for creating mugs and bowls

Your feasible region for this problem has 5 sides and therefore 5 vertices. (Some people call the vertices corner points.) Find the coordinates for the 5 vertices.

Now look back to question 3. The objective for this problem was to maximize revenue and you wrote an expression for what we wanted to maximize. Set this expression equal to R and we will call this our objective function. (Note: R was selected because revenue starts with R)

Write your objective function: R =

Use the vertices of the feasible region and your objective function to determine how many mugs and bowls should be made to maximize revenue.

What vertices gives use a maximum profit?

Perhaps you used your graphing utility to find the coordinates of some of the vertices. How could you find the coordinates without using a graphing utility? Explain how to find at least one set of vertices without graphing.