# The quadratic production function

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The harvesting of coffee is characterized by a quadratic production schedule as follows:

No. of Coffee

Laborers harvested

in kgms

0 0

1 200

2 450

3 620

4 780

5 850

6 920

7 950

8 980

9 1000

10 950

If the wage rate is $100 a day and the price of green coffee is $5.00 per kgm, find

(a) the quadratic production function,

(b) the optimum number of laborers to hire and (c) the maximum profit.

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#### Solution Preview

Answer:

The quadratic production function is given by

, (1)

where Q = the quantity and L = number of laborers.

The production function can be estimated by the method of least squares by solving the following normal equations:

(2)

(3)

(4)

Where and

...

#### Solution Summary

The quadratic production function is applied in this case.

$2.49