A winery has the following capacity to produce an exclusive dinner wine at either of its two vineyards at the indicated costs:

Vineyard	Capacity	Production Cost per Bottle
1	3,500 bottles	$23
2	3,100 bottles	$25

Four Italian restaurants around the country are interested in purchasing this wine. Because the wine is exclusive, they all want to buy as much as they need but will take whatever they can get. The maximum amounts required by the restaurants and the prices they are willing to pay are summarized in the following table.

Restaurant	Maximum Demand	Price
1	1,775 bottles	$69
2	2,275 bottles	$66
3	1,275 bottles	$70
4	1,725 bottles	$68

The costs of shipping a bottle from the vineyards to the restaurants are summarized in the following table.

	Restaurant
Vineyard	1	2	3	4
1	$7	$8	$13	$9
2	$12	$7	$8	$6

The winery needs to determine the production and shipping plan that allows it to maximize its profits on this wine. (Let

X_ij be the number of bottles produced at vineyard i to restaurant j.)

(a) Formulate an LP model for this problem to maximize profit (in dollars).

MAX:

Subject to:

Vineyard 1 Production:_______

Vineyard 2 Production:_______

Restaurant 1 Demand:_______

Restaurant 2 Demand:_______

Restaurant 3 Demand:_______

Restaurant 4 Demand:_______

X_ij 0

(b)

Create a spreadsheet model for this problem and solve it using Solver. What is the optimal solution?

(X₁₁, X₁₂, X₁₃, X₁₄, X₂₁, X₂₂, X₂₃, X₂₄) = __________