Question

You have realized that the number of plants, y, that you can grow in your garden, depends on the amount of fertilizer, f, and water, h. 1 In fact, you have noticed that your plants need twice as much fertilizer as water, and using any other ratio leads to input being wasted. Suppose that each unit of fertilizer costs w1 and each unit of water costs w2.

What might be your production function?

Answer 1

The production function for growing plants in a garden is based on the input amounts of fertilizer and water, where twice as much fertilizer as water is needed. The cost of producing plants is calculated by the quantity and cost of these inputs.

Step-by-step explanation:

The student's question involves determining a production function for the number of plants that can be grown in a garden based on the inputs of fertilizer and water. Given the relationship that a plant needs twice as much fertilizer as water, and considering the respective costs of fertilizer and water, the production function would be determined by these input quantities and their costs.

The production function can be visualized as an equation where the output, y (number of plants), is a function of the input amounts, f (fertilizer) and h (water). Since the plants need twice as much fertilizer as water, we could express this as f = 2h. Therefore, the cost to produce y plants would be the sum of the cost of fertilizer, which is f multiplied by w1, and the cost of water, which is h multiplied by w2.

The production function that represents the number of plants, y, that can be grown in your garden based on the amount of fertilizer, f, and water, h, can be expressed as:

y = 2h

This means that for every unit of water, you will need 2 units of fertilizer to maximize plant growth. Any other ratio of fertilizer to water will result in wasted input.