Question

A utility function is a function that attaches a measure to the satisfaction or utility a consumer gets from the consumption of products per unit time. Suppose U (x, y, z)= xyz is the utility function for 3 products, A, B, and C, with x, y, and z representing the number of units of 3 different products, respectively. The prices of these three products are pa, pe, and pc, in dollars, given by: PA=1 Pa = 2 Pc =1 Find the values of x, y, and that will maximize U (x, y, z)= xyz, subject to the condition that you must purchase $600 worth of products. In other words, P.X+ Pey+ Pez=600, with x, y, and z>0.