Hill Industries had sales in $2021$ of $$6,800,000$ and gross profit of $$1,100,000.$ Management is considering two alternative budget plans to increase its gross profit in $2022.$ Plan A would increase the unit selling price from $$8$ to $$8\mathrm{.}4.$ Sales volume would decrease by $10\%$ from its $2019$ level. Plan B would decrease the unit selling price by $O$\mathrm{.}5.$ The marketing department expects that the sales volume would increase by $100,000$ units. At the end of $2021,$ Hill has $40,000$ units of inventory on hand. If Plan A is accepted, the $2022$ ending inventory should be equal to $5\%$ of the $2020$ sales. If Plan B is accepted, the ending inventory should be equal to $60,000$ units. Each unit produced will cost $$1\mathrm{.}80$in direct labor, $$1\mathrm{.}40$ in direct materials, and $$1\mathrm{.}20$ in variable overhead. The fixed overhead for $2022$ should be $$1,895,000.$ Prepare a sales budget for $2022$ under each plan. Prepare a production budget for $2020$under each plan. Compute the production cost per unit under each plan. Why is the cost per unit different for each of the two plans? $($Round to two decimal places$)$ Which plan should be accepted? $($Hint: Compute the gross profit under each plan.$)$