A paper recycling company converts newspaper, mixed paper, white office paper, and cardboard into pulp for newspaper, packaging paper, and print stock quality paper. The following table summarizes the yield for each kind of pulp recovered from each ton of recycled material. Recycling Yield Newsprint Packaging Print Stock Newspaper 85% 80% --- Mixed Paper 90% 80% 70% White Office Paper 90% 85% 80% Cardboard 80% 70% --- For instance, a ton of newspaper can be recycled using a technique that yields 0.85 tons of newsprint pulp. Alternatively, a ton of newspaper can be recycled using a technique that yields tons of packaging paper. Similarly, a ton of cardboard can be recycled to yield 0.8 tons of newspaper or 0.7 tons of packaging paper pulp. Note that newspaper and cardboard cannot be converted to print stock pulp using the techniques available to the recycler. Processing cost per ton Purchase cost per ton Tons Available Newsprint Packaging Print Stock Newspaper $6.5 $11 --- $15 600 Mixed Paper $9.75 $12.25 $9.5 $16 500 White Office Paper $4.75 $7.75 $8.5 $19 300 Cardboard $7.5 $8.5 --- $17 400 The recycler wants to determine the least costly way of producing 500 tons of newsprint pulp, 600 tons of packaging paper pulp, and 300 tons of print stock quality pulp. Create a spreadsheet model for this problem and solve it. What is the optimal solution?
A paper recycling company converts newspaper, mixed paper, white office paper, and cardboard into pulp for newspaper, packaging paper, and print stock quality paper. The following table summarizes the yield for each kind of pulp recovered from each ton of recycled material.
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|
Recycling Yield |
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|
|
Newsprint |
Packaging |
Print Stock |
|
Newspaper |
85% |
80% |
--- |
|
Mixed Paper |
90% |
80% |
70% |
|
White Office Paper |
90% |
85% |
80% |
|
Cardboard |
80% |
70% |
--- |
For instance, a ton of newspaper can be recycled using a technique that yields 0.85 tons of newsprint pulp. Alternatively, a ton of newspaper can be recycled using a technique that yields tons of packaging paper. Similarly, a ton of cardboard can be recycled to yield 0.8 tons of newspaper or 0.7 tons of packaging paper pulp. Note that newspaper and cardboard cannot be converted to print stock pulp using the techniques available to the recycler.
|
|
|
Purchase cost per ton |
Tons Available |
||
|
|
Newsprint |
Packaging |
Print Stock |
||
|
Newspaper |
$6.5 |
$11 |
--- |
$15 |
600 |
|
Mixed Paper |
$9.75 |
$12.25 |
$9.5 |
$16 |
500 |
|
White Office Paper |
$4.75 |
$7.75 |
$8.5 |
$19 |
300 |
|
Cardboard |
$7.5 |
$8.5 |
--- |
$17 |
400 |
The recycler wants to determine the least costly way of producing 500 tons of newsprint pulp, 600 tons of packaging paper pulp, and 300 tons of print stock quality pulp.
- Create a spreadsheet model for this problem and solve it.
- What is the optimal solution?
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