Find the solution of the objective function for problems (a) - (b) below. For each problem,
confirm that the optimum satisfies the Kuhn-Tucker conditions. At each solution, describe
whether the constraint(s) is binding.
a) Minimize the function
![c = 5x^(2) - 80x + y^(2) - 32y](https://img.qammunity.org/2020/formulas/mathematics/middle-school/yuvi2q14pufaz35670sajlhusbrvt36o.png)
subject to the constraints
![x,y\geq 0](https://img.qammunity.org/2020/formulas/mathematics/college/g948wpxyv7nsrnoe6861fu63n1ii42l40j.png)
and
![x+y\geq 20](https://img.qammunity.org/2020/formulas/mathematics/middle-school/4m6fdrczwswq72q15fhm8hyblmdmtny4.png)
b) Maximize the profit function
![\pi = 50x +10y](https://img.qammunity.org/2020/formulas/mathematics/middle-school/rn2id6rly3398m0mkexwsaeanxc9tq62.png)
subject to the constraints
![x,y \geq 0](https://img.qammunity.org/2020/formulas/mathematics/high-school/oca53xgai88a2doc5hkhip7i41wo8stnex.png)
and
![x-y\leq 3](https://img.qammunity.org/2020/formulas/mathematics/middle-school/jedzo790txelmkqeaxrx6cwral8g23t4.png)
and