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Rework problem 3 in section 1 of Chapter 7 of your textbook about the Natural Fertilizer Company using the following data:

- The company produces 100-pound sacks of two types of fertilizer:
- Lawn fertilizer: 35-20-10 (percentage by weight of nitrate, phosphate, and potash)
- Garden fertilizer: 10-14-16 (percentage by weight of nitrate, phosphate, and potash)

- Available resources:
- 13 tons of nitrate
- 8 tons of phosphate
- 9 tons of potash

- Profit per sack:
- Lawn fertilizer: $10.00
- Garden fertilizer: $11.00

How many sacks of each type of fertilizer should the company produce to maximize its profit?

Answer :

Answer:

please find attached

Explanation:

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Rewritten by : Barada

Final answer:

This is a linear programming problem. We denote the number of sacks of lawn and garden fertilizer as x and y, and list constraints based on the available materials. Then, maximize the profit within these constraints using a graphing method.

Explanation:

This problem is a case of linear programming, which is a mathematical approach for determining a way to achieve the best outcome. The question is asking how many sacks of each type of fertilizer should the Natural Fertilizer Company produce with the given amount of nitrate, phosphate, and potash to maximize their profit.

To solve this, let's denote the number of sacks of lawn fertilizer and garden fertilizer produced as x and y, respectively. The constraints based on the available materials are as follows:

  • 35x + 10y <= 13 * 2000 (as one ton equals 2000 pounds)
  • 20x + 14y <= 8 * 2000
  • 10x + 16y <= 9 * 2000

We can then say our goal is to maximize the profit P = 10x + 11y. From here, you'll need to graph these inequalities and find the feasible region and its vertices. Then, substitute these vertices into the profit function, and the coordinates that result in the highest value is your optimal solution.

Learn more about Linear Programming here:

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