Jon Snow, an avid indoor gardener, has found that the number of happy plants, h, depends on the amount of light l and water w. In fact, Jon noticed that plants require three times as much light as water, and any more or less is wasted. Thus, Jon's production function is h = min{l, 3w}. The cost of light is denoted by pl and the cost of water by pw
a) Suppose Jon is using 1 unit of light, what is the least amount of water he can use and still produce a happy plant?
b) Find the cost function if Jon wants to minimize costs.
- l (pl, pw, h) =
- w (pl, pw, h) =
- c(pl, pw, h) =
c) Suppose Jon wants to produce 4 happy plants. What are the minimum amounts of light and water required? What is the cost of these four plants?