solve the question

A pipeline engineer working in Kuwait for the oil giant BP wants to perform a present worth analysis on alternative pipeline routings-the first predominately by land and the second primarily undersea. The un- dersea route is more expensive initially due to extra corrosion protection and installation costs, but cheaper security and maintenance reduces annual costs. Per- form the analysis for the engineer at 15% per year.Two manufacturers supply MRI systems for medi- cal imaging St. Jude's Hospital wishes to replace its current MRI equipment that was purchased & years ago with the newer technology and clarity of a state- of-the-art system. System K will have a first cost of $1,600,000, an operating cost of $70,000 per year, and a salvage value of $400,000 after its 4-year life. System L will have a first cost of $2,100,000, an operating cost of $50,000 the first year with an ex- pected increase of $3000 per year thereafter, and no salvage value after its 8-year life. Which system should be selected on the basis of a future worth analysis at an interest rate of 12% per year?A fast-food restaurant operates both a drive-through facility and a walk-in facility. On a randomly selected day, let X and Y, respectively, be the proportions of the time that the drive-through and walk-in facilities are in use, and suppose that the joint density function of these random variables is f(z,y) = (x+ 2y), OS=$1, 0Sys1, elsewhere. a) Find the marginal density of X. b) Find the marginal density of Y. c) Find the probability that the drive-through facility is busy less than one-half of the time.The proportion of the budget for a certain type of industrial company that is allotted to environmental and pollution control is coming under scrutiny. A data collection project determines that the distribution of these proportions is given by f(y) = 5(1-V)'. OSys1. elsewhere. (a) Verify that the above is a valid density function. (b) What is the probability that a company chosen at random expends less than 10% of its budget on environmental and pollution controls? (c) What is the probability that a company selected at random spends more than 50% of its budget on environmental and pollution controls?\f\f