$3.$ A material handler$$s job is to move raw materials to work stations. A manager must decide how many material handlers to hire in order to minimize the sum of employee costs and assembly line waiting costs. A study performed shows line workers waiting for material costs the company $$70$ per hour, material handlers earns $$18$ per hour and each material handler uses equipment that is estimated to cost $$12$ per hour. b$.$ An idea to invest in newer and faster carts is suggested to the manager. The new carts would allow an average of $10\mathrm{.}7$ requests to be met every hour. The hourly increase to the equipment cost would be $$10,$ making it $$22$ per hour. Would this be a good investment?