Jordan Boat Company makes inexpensive aluminum fishing boats. Production is seasonal, with considerable activity occurring in the spring and summer. Sales and production tend to decline in the fall and winter months. During year $2,$ the high point in activity occurred in June when it produced $204$ boats at a total cost of $$165,200.$ The low point in production occurred in January when it produced $34$ boats at a total cost of $$53,000.$

Required

a$.$ Use the high$-$low method to estimate the amount of fixed cost incurred each month by Jordan Boat Company.

b$.$ Determine the total estimated cost if $160$ boats are made.