A rock company uses five types of rocks to fill four orders. The phosphate content, availability of each type of rock, and the production cost per pound for each rock are listed below, as well as the size of each order and the minimum and maximum phosphate percentage in each order. What is the cheapest way to fill the orders? (Hint: this is a blending problem which will require you to constrain the weighted average)
| Rock type |
Cost |
% phosphate |
Amount |
| A |
$1.00 |
2.0% |
500 |
| B |
$5.00 |
5.0% |
600 |
| C |
$5.50 |
4.5% |
700 |
| D |
$2.00 |
3.0% |
400 |
| E |
$1.20 |
6.0% |
450 |
| Order |
1 |
2 |
3 |
4 |
| Size |
500 |
600 |
500 |
350 |
| Min % phosphate |
3.5% |
3.8% |
4.0% |
3.6% |
| Max % phosphate |
4.4% |
4.6% |
4.7% |
4.8% |