$5$ workers work $8$ hours a day for $5$ days to produce $4,000$ shopping carts. $5\%$ of shopping carts produced are defective $($so$,$ not usable$).$ Besides labor, the production also requires $20$ hours of machine work and $$9,000$ of material. One machine hour costs $$75,$ workers are paid $$15$ per hour, and total overhead is $$4,500.$ Find multi$-$factor productivity.