$2$PROBLEM $20\mathrm{.}14$ Setting Sales Price and Computing the Break$-$Even Point $$ LO$20-4,$ L$020-5,9$ LO$20-6,9$L$020-7$Ionic Charge is a newly organized manufacturing business that plans to manufacture and sell $50,000$ units per year of a new product. The following estimates have been made of the company's costs and expenses $($other than income taxes$)$:FixedVarlable per UnitManufacturing costs:Direct materialsDirect laborManufacturing overheadPeriod costs:Selling expensesAdministrative expensesTotals$ $900,000$$$4021163600\mathrm{.}000$$$1\mathrm{.}500\mathrm{.}000580$Instructionsa. What should the company establish as the sales price per unit if it sets a target operating income of $$500,000$ by producing and selling $50,000$ units during the first year of operations? $($Hint: First compute the required contribution margin per unit.$)$b$.$ At the unit sales price computed in part a$,$ how many units must the company produce and sell to break even? $($Assume all units produced are sold.$)$c$.$ What will be the margin of safety $($in dollars$)$ if the company produces and sells $50,000$ units at the sales price computed in part a$?$d$.$ Assume that the marketing manager thinks that the price of this product must be no higher than $$100$ to ensure market penetration.Will setting the sales price at $$100$ enable Ionic Charge to break even, given the plans to manufacture and sell $50,000$ units? Explain your answer.