# Math Help - Linear and Goal Programming Problem

1. ## Linear and Goal Programming Problem

Hello guys, I'm new here. I have a problem regarding the assignment that my prof gave it to me. He wants me to answer these difficult question which I had a hard time in analyzing the problem. Here is the link of the question:
http://faculty.salisbury.edu/~tvbanks/AppE.pdf

For case 2-3:
I have no idea how does the production of the 1st quarter affect the next quarter since you really need to know the answer the production of first quarter to answer the next quarter. The problem is the 1st quarter is unknown and I have difficulty in developing the constraints.

Case 8-1:
Really have a hard time in understanding this statement:
To guarantee sustained future production, each acre of reforestation in each alternative
requires that as many acres as years in rotation be assigned to that alternative.

(I post the attachment what I did so far for 8-1)
Pls check it and help me to analyze the constraint for the third objectives.

Oh yeah, I used excel and data solver to answer this.

Thank you very much for your time and I really appreciate if you could help me to analyze and understand the case.

2. Btw, this the question for:

Case 2-3
ArkTec assembles PC computers for private clients.The orders for the next four quarters
are 400, 700, 500, and 200, respectively.ArkTec has the option to produce more than
is demanded for the quarter, in which case a holding cost of $100 per computer per quarter is incurred. Increasing production from one quarter to the next requires hiring additional employees, which increases the production cost per computer in that quarter by$60. Also, decreasing production from one quarter to the next would require laying
off employees, which results in increasing the production cost per computer in that
quarter by $50. How should ArkTec schedule the assembly of the computers to satisfy the demand for the four quarters? Case 8-1 The Warehouzer Company manages three sites of forest land for timber production and reforestation with the respective areas of 100,000, 180,000, and 200,000 acres.The main timber products include three categories: pulpwood, plywood, and sawlogs. Several reforestation alternatives are available for each site, each with its cost, number of rotation years (i.e., number of years from seedling size till harvesting), return from rent, and production output. Table E.23 summarizes this information. To guarantee sustained future production, each acre of reforestation in each alternative requires that as many acres as years in rotation be assigned to that alternative. The rent column represents the stumpage value per acre. The goals of Warehouzer are: 1. Annual outputs of pulpwood, plywood, and sawlogs are 200,000, 150,000, and 350,000 cubic meters, respectively. 2. Annual reforestation budget is$2.5 million.

3.
Annual return from land rent is $100 per acre. How much land at each site should be assigned to each alternative? TABLE E.23 Annual$/acre Annual
Rotation
Site Alternative
Cost Rent yr Pulpwood Plywood Sawlogs

1
A1 1000 160 20 12 0 0

A
2 800 117 25 10 0 0

A
3 1500 140 40 5 6 0

A
4 1200 195 15 4 7 0

A
5 1300 182 40 3 0 7

A
6 1200 180 40 2 0 6

A
7 1500 135 50 3 0 5
2
A1 1000 102 20 9 0 0

A
2 800 55 25 8 0 0

A
3 1500 95 40 2 5 0

A
4 1200 120 15 3 4 0

A
5 1300 100 40 2 0 5

A
6 1200 90 40 2 0 4
3
A1 1000 60 20 7 0 0

A
2 800 48 25 6 4 0

A
3 1500 60 40 2 0 4

A
4 1200 65 15 2 0 3

A5 1300 35 40 1 0 5

3. ## Solution to the problem

Hi, I have the same problem to answer and I'm stuck. I cannot solve it.

Does someone get the solution please?

teachers like to torture students...