William Lake Forest Products (WLFP) 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 in 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 of sawmill-quality wood, 40% grades out as plywood-quality wood, and 30% grades out as pulp-quality wood.

Sawmill-quality wood can be sold, sent to the sawmill for sawing into lumber, 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 product 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 processes wood in batches of 150,000 units. The cost per batch processed in the plywood mill is $75,000 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 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 int he 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 plywood mill is $.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 batches that can be sold during the upcoming period each of the commodities is:

Saw logs unprocessed     500

Plywood logs unprocessed 750

Pulp logs unprocessed 400

Saw logs processed 1500*

Plywood logs processed 3000

Pulp logs processed 4500

This number represents the maximum amount of sawmill products that can be sold based on processing 1500 batches of raw logs.

What is the optimal production plan?