Question

A local nursery sells a large number of ornamental trees every year. The owners have determined the cost per tree C for buying and caring for each tree before it is sold is C = 0.001n2 - 0.3n + 50. In this function, C is the cost per tree in dollars and n is the number of trees in stock.
a. How many trees will minimize the cost per tree?
b. What will the minimum cost per tree be?

Answer 1

The minimum cost is achieved when 150 trees are produced giving a minimum cost of $27.5

Polynomial is an expression that involves the operations of addition, subtraction, multiplication of variables.

Let C represent the cost for buying and caring for n trees. Given that:

C = 0.001n² - 0.3n + 50.

The minimum cost is at dC/dn = 0, hence:

dC/dn = 0.002n - 0.3

0.002n - 0.3 = 0

0.002n = 0.3

n = 150

C(150) = 0.001(150)² - 0.3(150) + 50 = 27.5

The minimum cost is achieved when 150 trees are produced giving a minimum cost of $27.5

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