Define each variable

$$ Write the objective function and constraints.

$$ Solve using an online solver and write the conclusion in a complete sentence

$4.$ A&P can buy at most $60$ packages of three different brands of cheese. The first brand

costs $$2$ per package, the second brand costs $$3$ per package, and the third brand costs

$$4$ per package. A&P can spend up to $$120$ on cheese. The profit for A&P is $$3$ for

the first brand, $$3$ for the second brand, and $$4$ for the third brand.

a$)$ How many packages of each brand of cheese should A&P buy in order to

maximize profit?

b$)$ What is the maximum profit?