I am having difficulty with the following problem :
A lecturer eats only two types of food and has a salary I > 0 . The quality of his lectures is given by x1^a1 * x2^a2 , where xi is the daily consumption of food i, respectively, and a i > 0 are constants, i = 1, 2 , a with a1 + a2 = 1 . The price of food i is pi > 0 , i = 1, 2 . The lecturer wishes to give lectures that are
of quality as high as possible, without spending more than his income. What is the optimal food consumption? If the salary is increased, after recent presidential elections, with ∆I , how much of an increase of the quality of lectures can be expected?
Can someone help please?