The Boatwright Sauce Company is a small manufacturer of several different sauces to use in food products. One of the products is a blended sauce mix that is sold to retail outlets. Joy Boatwright must decide how many cases of this mix to manufacture each month. The probability that the demand will be six cases is 0.1, for seven cases is 0.5, for eight cases is 0.3, and for nine cases is 0.1. The cost of every case is $55, and the price that Joy gets for each case is $90. Unfortunately, any cases not sold by the end of the month are of no value, due to spoilage. How many cases of sauce should Joy manufacture each month?