Moonbucks, a coffee shop, sells three blends of coffee. They use three varieties of coffee beans to make the three blends. Although the recipes for the three blends are not fully precise, certain "golden rules of coffee blending" must be satisfied when combining the three varieties: -Blend 1 should contain no more than 20% of Variety 1 (by weight) -Blend 2 should contain at least 30% of Variety 2 (by weight) -Blend 3 should contain at least 70% of Varieties 2 and 3 combined (by weight) Furthermore, there is limited availability of the three varieties. The maximum weekly avail- ability of Varieties 1, 2 and 3 are 8000 lbs, 10,000 lbs and 9000 lbs, respectively and weekly processing capability of the coffee roaster is 25,000 lbs. To satisfy the weekly needs of the customers, at least 5000 lbs of Blend 1 should be prepared. Given that the three varieties cost 1.20S, 1.30$ and 1.10$ per lb respectively and the selling price for the blends are 3$, 3.20$ and 2.80$ per lb respectively, the manager would like to know the number of lbs of each variety to be used in each blend in order to maximize profit. Formulate a linear programming problem to help the manager.