Three Ships Winery produces two different wine blends. A batch of the Dark Night blend uses 4 tons of malbec grapes, 2 tons of merlot grapes, and 4 tons of nebbiolo grapes. A batch of the Morning Star blend uses 3 tons of trebbiano grapes, 6 tons of merlot grapes, and 1 ton of malbec grapes. The winery has a total of 16 tons of malbec grapes, 18 tons of merlot grapes, 8 tons of trebbiano grapes, and 16 tons of nebbiolo grapes. Each batch of wine requires 5 cubic yards of aging and storage space. The Dark Night blend requires 12 hours processing time per batch, while the Morning Star blend requires only 10 hours. The winery has a total of 50 hours of processing time available, and 35 cubic yards of aging and storage space. The profit for a batch of Dark Night is $14,500 and the profit for a batch of Morning Star is slightly less at $12,250. How many batches of each type of wine should the winery produce this year to maximize its profit under these conditions? Additionally, what is the maximum profit possible if the winery wants to make at least three batches of Dark Night, but is willing to create half-batches of wine if necessary? Formulate a linear programming model and solve it graphically. Display your graph and calculate the maximum profit. Create your graph using Microsoft Word or Excel