4. Consider the problem maximise
subject to ​
− 2
1
​
x 2
− 2
1
​
y 2
+25x+30y
3x+2y≤10
x≥0,y≥0
​
(a) Verify that the objective function is concave. [4 marks ] (b) Derive the modified linear program from the Kuhn-Tucker conditions. [8 marks] (c) Find the solution of the modified linear program in (b) by using the modified Simplex Method clearly stating the reasons for your choice of entering and leaving variables. [15 marks ] (d) Explain why the solution of the modified linear program is the solution of the original maximisation problem [3 marks]