$6.$ A manufacturer produces gas grills that sell for $$400$ each. The average cost

function for grill production is C$($x$)=525,000/$x $-20+0.012$x$.$ If production is limited to $20,000$ grills, find the number of grills that should be produced and sold to maximize profit.

$7.$ A fence must be built to enclose a rectangular area of $20,000$ square feet. Fencing material costs $$3$ per foot for the sides facing north and south, and $$6$ per foot for the sides facing east and west. Find the cost of the least expensive fence.

$8.$ The demand for Super Titan tires is $900,000$ per year. It costs the manufacturer

$$4000$ to prepare a production run and $$20$ to produce each tire. The storage cost

is $$2$ per tire per year. Find the number of tires that should be produced in each

run so that total costs of production and storage are minimized.