A factory produces Brand A dog food and Brand B dog food. It must
produce no more than 4 tons of Brand A every day, and at least 2 tons of
Brand B every day. The factory must produce at least 4 tons of Brand A
for every 5 tons of Brand B (the ratio of Brand A to Brand B must be at
least , and the factory cannot produce more than 8 tons of
total dog food in a day.

Brand A costs 1 thousand dollars per ton to make, and sells for 2
thousand dollars per ton. Brand B costs 2.5 thousand dollars to make,
and sells for 3 thousand dollars per ton. Thus, the equation for
revenue is *R* = 2*x* + 3*y*, the equation for cost is *C* = *x* + 2.5*y*, and
the equation for profit is *P* = *R* - *C* = *x* + 0.5*y*.

**Problem : **
How much of each brand should the factory make to maximize revenue?

tons of Brand A, and

tons of Brand B.

**Problem : **
How much of each brand should the factory make to minimize cost?

tons of Brand A, and

2 tons of Brand B.

**Problem : **
How much of each brand should the factory make to maximize profit?

4 tons of Brand A, and

4 tons of Brand B.

The school cafeteria carries hot dogs and hamburgers. They cannot make
more than 400 hot dogs in a single day. The cafeteria must make at
least half as many hamburgers as hot dogs, but cannot make more than
one-fourth the number of hot dogs plus 200. In addition, the number of
hot dogs plus twice the number of hamburgers must be at least 400.

Hot dogs cost 10 cents to make, and the cafeteria sells them for 20
cents each. Hamburgers cost 60 cents to make, and the cafeteria sells
them for 50 cents each.

**Problem : **
How many of each item should the cafeteria make in order to have the
highest revenue? What is the maximum amount of revenue the cafeteria
can make?

400 hot dogs, 300 hamburgers. Revenue = $230.

**Problem : **
How many of each item should the cafeteria make in order to minimize the
cost? What is the minimum amount of money the cafeteria must spend?

200 hot dogs, 100 hamburgers. Cost = $80.

**Problem : **
How many of each item should the cafeteria make in order to maximize the
profit? What is the maximum profit?

400 hot dogs, 200 hamburgers. Profit = $20.