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