Question: a factory makes a product out of three infinitely divisible...

A factory makes a product out of three infinitely- divisible ingredients X, Y , and Z. The ingredients cost p, q, and r pounds per kg, respectively, with p, q, r > 0 all different, and the factory has a budget of B > 0 pounds. The value of the product is some function g(x, y, z)=exp(x+y+z). of the weight of the ingredients. Solve this problem when the factory wishes to maximize the value of their product, within their budget.