Veluwe Forest Company (VFC) is an integrated paper products firm. Planning for the period's activities begins with the wood lot. The maximum amount of raw wood that can be harvested during this period is 10,000,000 units. Wood is harvested in batches of 1,000,000 units. The cost of harvesting is 300,000 per batch plus 2 per unit of wood harvested.

When the raw wood has been harvested, it is graded. On average, about 30% of the raw wood harvested grades out as samill-quality wood, 40% grades out as plywood (multiplex) quality wood, and 30% grades out as pulp-quality wood.

Sawmill-quality wood can be sold, sent to the sawmill for sawing into lumber (timmerhout), or downgraded into plywood-quality wood. Sawmill-quality wood can be sold on the open market in batches of 1,000 units for 3,000 per batch.

The sawmill processes wood in batches of 100,000 units. The cost per batch processed in the sawmill is 60,000 plus 1.50 per unit of wood processed. The capacity of the sawmill is limited, by the availability of saws, to 2,000,000 units of wood, or 20 batches. Each 1,000 units of wood processed through the sawmill yields products that can be sold for 5,000.

The plywood-quality wood can be sold, downgraded to pulp-quality wood, or sent to the plywood mill to be made into plywood. Plywood-quality wood can be sold in the open market in batches of 1,000 units for 2,500 per batch.

The plywood mill process wood in batches of 150,000 units. The cost per batch processed in the plywood mill is 75,000 plus 2.50 per unit of wood processed. The capacity of the plywood mill is limited by the capacity of the peeling (ontharing) operation to 3,000,000 units of wood, or 20 batches. Each 1,000 units of wood processed through the plywood mill yields product that can be sold for 6,000.

The pulp-quality wood can be sold or sent to the paper mill to be made into various paper and cardboard products. Pulp-quality wood can be sold in the open market in batches of 1,000 units for 2,000 per batch.

The paper mill processes wood continuously, and thus no batching operation occurs in this mill. The variable cost per unit of wood processed in the plywood mill is 0.80. The capacity of the paper mill is limited to 5,000,000 units of wood. Each 1,000 units of wood processed through the paper mill yields product that can be sold for 3,500.

The marketing department has advised that the maximum number of 1,000 unit batches that can be sold during the upcoming period of each of the commodities is:

Marketing constraints per batch of 1,000 units

Raw saw logs 500

Saw mill products 1,500

Raw plywood 750

Plywood mill products 3,000

Raw pulp logs 400

Paper mill products 4,500

Required:

1. Formulate an LP model to help VFC determine its best production plan for the upcoming period.
2. What is the optimal production plan?