$87..$ During the next four quarters, Dorian Auto must meet $($on time$)$ the following demands for cars: $4000$ in quarter $1$;$2000$ in quarter $2$; $5000$ in quarter $3$; $1000$ in quarter $4.$ At the beginning of quarter $1,$ there are $300$ autos in stock. The company has the capacity to produce at most $3000$ cars per quarter. At the beginning of each quarter, the company can change production capacity. It costs $$100$ to increase quarterly production capacity by one unit. For example, it would cost $$10,000$ to increase capacity from $3000$ to $3100.$ It also costs $$50$ per quarter to maintain each unit of production capacity $($even if it is unused during the current quarter$).$ The variable cost of producing a car is $$2000.$ A holding cost of $$150$ per car is assessed against each quarter's ending inventory. At the end of quarter $4,$ plant capacity must be at least $4000$ cars.

a$.$ Determine how to minimize the total cost incurred during the next four quarters.

b$.$ Use SolverTable to determine how much the total cost increases as the required capacity at the end of quarter $4$ increases $($from its current value of $4000).$