Lawn Rich, Inc., makes four different lawn care products that have fixed percents of phosphate, nitrogen, potash, and other minerals. The following table shows the percent of each of the four ingredients in each of Lawn Rich’s products and the profit per ton for each product.

A lawn care company buys in bulk from Lawn Rich and then blends the products for its own purposes. For the blend it desires, the lawn care company wants its Lawn Rich order to contain at least 35 tons of phosphate, at most 20 tons of nitrogen, at most 9 tons of potash, and at most 4 tons of other minerals. How many tons of each product should Lawn Rich produce to fulfill the customer’s needs and maximize its own profit? What is the maximum profit?

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Product Product Product Product 1 2 3 4 % Phosphate 60 30 20 10 % Nitrogen 20 20 20 20 % Potash 9 15 18 % Other minerals 8 3 2 1 Profit/ton $120 $150 $180 $210