pls answer all the questions

Problem $2 : Consider the following problem: Maximize 36X1+9X126X13+36X23X23 Subject to: X1+X23;X10;X20 Part a: Write out the Lagrangian function for this problem. (4 points) Part b: Write out the first order conditions of the Lagrangian function with respect to X1,X2 a ar the Lagrange multiplier. ( 6 points) Part c: Write out the KKT conditions for this problem. (4 points) Part d: Determine whether (X1,X2)=(1,2) can be optimal by applying the KKT conditions. ( 6 points) Problem \#3: Consider the following function: Y=37.68415.315X+3.095X20.218X3+0.005X4. Part a: Plot the function on an X-Y graph for positive values of X from 1 to 20 in EXCEL. ( 6 points) Part b: How many local maximum solutions are there (not counting the endpoints of the graph)? (4 points) Part c: How many local minimum solutions are there (not counting the endpoints of the graph)? (4 points) Part d. Use solver in EXCEL, to find the minimum value of Y using a starting value of X=3. What value of Y do you obtain? Noto: In order to start the GRG algorithm in EXCEL at a particular starting point, when you set-up your problem in a spreadsheet do not set your varrable cell (X) to 0 , but to the indicated value in the question (eg. 3 or 18 for the next part). ( 8 points) Part e: Use solver in EXCEL, to find the minimum value of Y using a starting value of X=18. What value of Y do you obtain? (4 points) Problem $2 : Consider the following problem: Maximize 36X1+9X126X13+36X23X23 Subject to: X1+X23;X10;X20 Part a: Write out the Lagrangian function for this problem. (4 points) Part b: Write out the first order conditions of the Lagrangian function with respect to X1,X2 a ar the Lagrange multiplier. ( 6 points) Part c: Write out the KKT conditions for this problem. (4 points) Part d: Determine whether (X1,X2)=(1,2) can be optimal by applying the KKT conditions. ( 6 points) Problem \#3: Consider the following function: Y=37.68415.315X+3.095X20.218X3+0.005X4. Part a: Plot the function on an X-Y graph for positive values of X from 1 to 20 in EXCEL. ( 6 points) Part b: How many local maximum solutions are there (not counting the endpoints of the graph)? (4 points) Part c: How many local minimum solutions are there (not counting the endpoints of the graph)? (4 points) Part d. Use solver in EXCEL, to find the minimum value of Y using a starting value of X=3. What value of Y do you obtain? Noto: In order to start the GRG algorithm in EXCEL at a particular starting point, when you set-up your problem in a spreadsheet do not set your varrable cell (X) to 0 , but to the indicated value in the question (eg. 3 or 18 for the next part). ( 8 points) Part e: Use solver in EXCEL, to find the minimum value of Y using a starting value of X=18. What value of Y do you obtain? (4 points)