Black Top Wine company produces two different wine blends. A batch of the Dark Night blend uses ...

Black Top Wine company 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. Formulate a LP model to solve the problem. Solve the model.