Mellow Mushroom makes two types of pizza: basic cheese $($cheese and tomatoes$)$ and vegetable $($cheese$,$ fomatoes, and basil$).$ Mellow Mushroom sells at least $60$ units a day of vegetable pizza, and at least $40$ units a day of basic cheese pizza. The cost of tomatoes and basil is $$2$ per unit for the vegetable pizza, and the cost of tomatoes is $$1$ per unit for the basic cheese pizza. No more than $$320$ per day can be spent on tomatoes and basil together. The cheese used for the vegetable pizza is $$3$ per unit, and the cheese for the basio cheese pizma is $$4$ per unit. Mellow Mushroom can spend no more than $$1,000$ per day on cheese. How many units of each pizza should Mellow Mushroom make to maximize revenue if the basic cheese pizza sells for $$15$ per unit and the vegetable pizza sells for $$24$ per unit?

a$.$ Clearly define the variables in this problem.

$x=$ Bosic

$y=$ Vegetable

b$.$ Fill in the chart completely.

$\backslash$table$[[,$Variable,Tomato & Basil Cost,Cheese Cost,Pizza Cost$],[$Basic Pizza,,,,$],[$Vegetable Pizza,,,,$],[$Constraints$,,,,]]$

c$.$ Clearly state the $4$ constraints $($all inequalities$)$ related to the feasible region.

d$.$ State the objective function.

e$.$ Use the graphical method to solve: Graph the solution region, showing the intercepts used. Label graph properly. Find and label all corner points. The grid for the graph is on the next page. Show all necessary work.

f$.$ How many units of each pizza should Mellow Mushroom make to maximize revenue if the basic pizza sells for $$15$ per unit and the vegetable pizza sells for $$24$ per unit? Write your answer in complete sentence$($s$).$

Compute the Maximum using the corner points.

Complete Sentence$($s$)$ Answer: