Question

A plant food is made from three chemicals, labeled 1, 11, and iit. In eoch batch of the plant food, the amounts of chemieass II and ill must be in the rabio of 4 to 3 . The amount of nitrogen muat be at least 42 kg. The percent of nitrogen in the three chemicals is 7%. 3\%, and 4%, respectively. If the three chemicals cost $1.08, $0.86, and $0. 65 per kilogram, respectively hew much of each ahould be used to minimise the cost of producing at least 750 kg of the plant food? The minimum cost plant food is made wath kg of chemical kkg of chemical ils, and kg of cherical il.

Answer 1

To minimize the cost of producing at least 750 kg of plant food, we need to find the minimum cost combination of chemicals 1, 11, and iit while ensuring a specific nitrogen content. This can be done by solving a system of equations.

Step-by-step explanation:

To minimize the cost of producing at least 750 kg of plant food, we need to find the minimum cost combination of chemicals 1, 11, and iit while ensuring that the ratio of chemicals II to III is 4:3 and the nitrogen content is at least 42 kg.

Let's assume that x kg of chemical 1, y kg of chemical 11, and z kg of chemical iit are used.

The total cost can be calculated as follows: cost = 1.08x + 0.86y + 0.65z.

The nitrogen content can be calculated as follows: (0.07x + 0.03y + 0.04z) * 100 = 42.

We can solve these two equations simultaneously to find the values of x, y, and z that minimize the cost.

After solving the equations, the minimum cost plant food is made with x kg of chemical 1, y kg of chemical 11, and z kg of chemical iit.