2. A local child opens a lemonade stand which sells both lemonade for $2 per glass and strawberrylemonade for $3 per glass. Every glass of lemonade takes 3 lemons and 1 cup of sugar. On the other hand a glass of strawberry-lemonade takes 2 lemons, 5 strawberries and 1 cup of sugar. On the first day of business, the child has 20 lemons, 35 strawberries, and 10 cups of sugar. The child understands some of linear programming and models the problem of maximizing profit by the following LP. Maximize 2x1+3x2 s.t. 3x1+2x220 5x235 x1+x210 x1,x20 where x1 represents the number of glasses of standard lemonade to make and x2 represents the number of glasses of strawberry-lemonade to make (assuming that every glass will sell). The optimal solution is found to be x1=2 and x2=7 which brings in $25. (a) As this child's parent, you want to help them make more money! Use your understanding of duality and sensitivity analysis to find the shadow price of each resource (lemons, strawberries, and sugar) at the optimal basis. (b) At the local farmers market one lemon costs $0.50, one strawberry costs $0.30 and a cup of sugar costs $0.10. Purchasing more of which one resource (lemons, strawberries, and sugar) would increase profit the most? How do you know? (c) Would buying more of any of the resources reduce profit? (d) How much sugar could you sell, before the current solution becomes infeasible. 2. A local child opens a lemonade stand which sells both lemonade for $2 per glass and strawberrylemonade for $3 per glass. Every glass of lemonade takes 3 lemons and 1 cup of sugar. On the other hand a glass of strawberry-lemonade takes 2 lemons, 5 strawberries and 1 cup of sugar. On the first day of business, the child has 20 lemons, 35 strawberries, and 10 cups of sugar. The child understands some of linear programming and models the problem of maximizing profit by the following LP. Maximize 2x1+3x2 s.t. 3x1+2x220 5x235 x1+x210 x1,x20 where x1 represents the number of glasses of standard lemonade to make and x2 represents the number of glasses of strawberry-lemonade to make (assuming that every glass will sell). The optimal solution is found to be x1=2 and x2=7 which brings in $25. (a) As this child's parent, you want to help them make more money! Use your understanding of duality and sensitivity analysis to find the shadow price of each resource (lemons, strawberries, and sugar) at the optimal basis. (b) At the local farmers market one lemon costs $0.50, one strawberry costs $0.30 and a cup of sugar costs $0.10. Purchasing more of which one resource (lemons, strawberries, and sugar) would increase profit the most? How do you know? (c) Would buying more of any of the resources reduce profit? (d) How much sugar could you sell, before the current solution becomes infeasible