Suppose that when a consumer purchases x units of one product, y of another and z of third, the utility of the purcases is given by: U = 5 · x ^{1/3} · y^{2/3} · y^{1/2}If the prices per unit are 2$, 5$ and 1$ and consumer has 100$ to spend. How many units of each should the consumer purchase in order to maximize utility?Hint: start typing random letters...