PLEASE SOLVE ALL. WILL GIVE YOU THUMBS UP$!!!!$

a$.$ Determine the total expected number of cars in the engine installation process and tire installation process.

b$.$Determine the total expected time that a car spends in the engine installation process and tire installation process $($in minutes$).$

c$.$What is the probability that there will be two cars in the entire workstation?

d$.$The manufacturing manager finds the waiting time in the tire installation process is too long. He is considering $2$ alternative proposals to improve the current system. Proposal $1$: Add another worker to the tire installation process. Two workers will be tasked to install tires to one car. Thus, it will cut the service time into half of the existing service time. A worker would cost them Php$35$ per hour.Proposal $2$: To buy a set of equipment that will automatically install the tires. The new equipment has a capitalized cost of Php$40$ per hour and will reduce installation time to $1$ minute. Each time a vehicle is stalled in the production area costs the company Php$8$ per minute. Compute the cost of the present system and the costs of the two proposals. What can you recommend to the company?

e$.$The supervisor of the engine installation process would like to provide enough space in for vehicles waiting for engine installation. In case the space is not enough, work in process will have to queue along an aisle in production area. How much space must be provided so that it will be that aisle will only be used at most $5\%$ of the time. A vehicle needs $8$ square feet. On the average, what is the percent utilization of the allocated waiting area?

f$.$After the car has been manufactured, it will be brought to the huge parking area for inspection. The inspection process takes some time to finish and follows normal

distribution with a mean of $6/$n minutes $($where n is the number of inspectors$).$ The inspection of each car is being performed by n number of inspectors.

f$\mathrm{.}1.$ What is the minimum number of inspectors for the system not to explode?What is the associated probability that there will be $3$ cars waiting to be inspected?

f$\mathrm{.}2.$ If there are six inspectors, there is a $10\%$ chance that they will finish their task in at least $2$ minutes. What is the probability that there would be $5$ cars in theparking area waiting for inspection?