A company has developed a new product. The demand for said product is unknown, so the company assumes that it is a uniformly distributed random variable [0,1,2,...,N]. The products must be made in advance, and each one sold produces a profit of g dollars while one left unsold produces a loss of p dollars. How many of these items must be produced in advance to maximize expected profit? Hint: Set up the function that models the gain and compute the expected value. Calculate the derivative to obtain the maximum profit.