Three Ships Winery produces two different wine blends. A batch of the Dark Night blend uses 4 tons of malbec grapes and 2 tons of merlot grapes. A batch of the Morning Star blend uses 2 tons of malbec grapes and 4 tons of merlot grapes. The winery has a total of 18 tons of malbec grapes, and 18 tons of merlot grapes.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, assuming half batches are allowed? Formulate a linear programming model and solve it graphically. Display your graph and calculate the maximum profit.