Develop a mathematical model for the total profit in terms of the price, P.

A manufacturer of kitchen appliances is preparing to set the price on a new blender. Demand is thought to depend on the price and is presented by the model D = 2,500 – 3P. The accounting department estimates that the total cost can be represented by C = 5,000 5D. Develop a mathematical model for the total profit in terms of the price, P.
With the growth of digital photography, a young entrepreneur is considering establishing a new business, Cruz Wedding Photography. He believes that the average number of wedding bookings per year is 15. One of the key variables in developing his business plan is the life he can expect from a single digital single-lens reflex (DSLR) camera before it needs to be replaced. Due to heavy usage, the shutter life expectancy is estimated to be 150,000 clicks. For each booking, the average number of photographs taken is assumed to be 2,000. Develop a model to predict the camera life (in years).
The owner of Cruz Wedding Photography believes that the average number of wedding bookings per year can be estimated by triangular distribution with a minimum of 10, maximum of 22, and most likely value of 15. One of the key variables in developing his business plan is the life he can expect from a single digital single-lens reflex (DSLR) camera before it needs to be replaced. Due to heavy usage, the shutter life expectancy is estimated by a normal distribution with a mean of 150,000 clicks with a standard deviation of 10,000. For each booking, the average number of photographs taken is assumed to be normally distributed with a mean of 2,000 and a standards deviation of 300. Develop a simulation model using 500 trials to determine summary statistics and the distribution of the camera life (in years).