The National Paper company contracts with their suppliers on a quarterly basis to buy pulp for their paper mills in Maine, Georgia, and Louisiana. The pulp comes from four suppliers in four regions: Western Canada, Brazil, Scandinavia, and the Pacific Northwest. The cost of purchasing the pulp (in US dollars per ton), the amount of pulp available, and the forecasted quarterly demand (in tons) for the next quarter are given in the tables below.

Supplier	Cost/ton	Availability(tons/quarter)
Canada	$1100	850000
Brazil	$950	950000
Scandinavia	$1000	1250000
deer	$1200	500000

Mill	Demand(tons/quarter)
Maine	900000
Georgia	1080000
Louisiana	960000

The cost of shipping pulp (per ton) using standard shipping containers is given in the table below.

Shipping costs (US Dollars per ton)
From \To	Maine	Georgia	Louisiana
Canada	$120	$150	$180
Brazil	$150	$130	$120
Scandinavia	$150	$180	$200
Pacific Northwest	$120	$150	$160

1a. Formulate a linear programming (LP) model to help National Paper acquire their pulp for the upcoming quarter.

1b. Solve your model in Excel and determine the optimal value and the optimal solution. Report your results.

Suppose the Scandinavian supplier alerts National Paper that they can no longer ship their pulp using standard storage containers due to a container shortage. As a result, the Scandinavian supplier has contracted cargo ships that can carry 30000 tons of pulp per cargo ship. They will only sell National Paper pulp in increments of a full cargo ship (i.e., in increments of 30000 tons), applying the same shipping costs (per ton) as given in the previous table.

1c. Revise your LP formulation to account for this new shipping requirement. Write out your formulation in its entirety.

1d. Solve your model in Excel to determine a new optimal acquisition schedule and a new optimal value. Report your results.