A company is selling a toy car this retail season. The fixed cost to produce the car is $120,000 while the variable cost is $40 per car. The company will sell the car for $48 each. The company decides to produce 50,000 cars. The company expects the number of customers who want to purchase a car (assume no customer purchases more than one) to be a normally distributed random variable with mean 55,000 and standard deviation of 9,000. Obviously, the company cant sell any more cars than it produces, but a wholesale distributor has agreed to purchase any surplus cars unsold after the retail season for $12 each.

a. Create a spreadsheet relating the production quantity, total production cost, customers, sales, revenue from sales, amount of surplus, revenue from sales of surplus, and net profit.

b. (12 pts) By doing 1000 simulations, find a 95% confidence interval for the companys profit.