If you wish to maximize expected profit, how many sandwiches should be produced each day?
Assume you produced 28 sandwiches. If you sold 28 your profit will be 28*3.5 – 28*2 = 42 $. So probability that you will make 42$ profit is 0.2. If you sell 29 sandwiches your profit will be the same, so the probability that you earn $42 profit is 0.3. Similarly if you sell 30 or 31 sandwiches. So when you produce 28 sandwiches your expected profit will be $42. Now assume you produced 29 sandwiches. If you sell 28 sandwiches you profit will be 3.5*28 – 2*29 = $40 with probability 0.2. If you sell 29 your profit will be 3.5*29 – 2*29 = $43.5 with probability 0.3 as well as 0.4 and 0.1. Therefore your expected profit (when you produce 29 sandwiches) is: 0.2*40 + 0.8*43.5 = $42.8. ETC. Little table below shows the numbers: prob:0.2..0.3….0.4…..0.1 sold:28…29……30……31 prod:……….profit…………. expected 28…42…42…42…42…..42 29..40..43.5..43.5..43.5..42.8 30…38..41.5..45..45…42.55 31…36..39.5..43..46.5..40.9 Therefore you maximum expected profit is 42.8 w
