1. [10 marks each] A rm has ve cement mixers for hire, the hire charge for each of which is $15.00 per day. The overheads are $5.00 per mixer per day, whether or not they are hired. Suppose the daily demand for cement mixers has a Poisson distribution with mean 4. (a) What is the probability that the rm makes a (strictly positive) prot on any given day? (b) What is the expect prot for each day? You may want to use the R function dpois. For all of the above, you must provide your mathematical derivations by hand. However, to calculate your nal answer, you can use R or (any other programming of your choice)