Optimal Cakes Production Problem

[YasserJoomun]

A cake seller prepares a certain number of cakes in the morning to be sold at the market daily. It costs him $3 to produce each cake, which he would then sell at a fix price of $10 each. Let's assume that the demand on a particular day for the cake at the market follows a normal distribution with mean 400 and standard deviation 50. If on a certain day, the number of cakes prepared exceeds the demand, the excess cakes will contribute to a loss, equal to the cost of production of the latter, whereas if the number of cakes prepared is less than the demand, potential sales are missed, and hence there is a trade off in determining a reasonable number of cakes to produce. What is the optimal number of cakes that the seller should prepare daily for him to expect maximum profit?