$9-41$ Absorption costing and production$-$volume variance$$alternative capacity bases. Energy Glow Light $($EGL$),$ a producer of energy$-$efficient light bulbs, expects that demand will increase markedly over the next decade. Due to the high fixed costs involved in the business, EGL has decided to evaluate its financial performance using absorption costing income. The production$-$volume variance is written off to cost of goods sold. The variable cost of production is $$2\mathrm{.}70$ per bulb. Fixed manufacturing costs are $$1,020,000$ per year. Variable and fixed selling and administrative expenses are $$0\mathrm{.}20$ per bulb sold and $$290,000,$ respec$-$tively. Because its light bulbs are currently popular with environmentally conscious customers, EGL can sell the bulbs for $$9\mathrm{.}60$ each.

EGL is deciding among various concepts of capacity for calculating the cost of each unit produced. Its choices are as follows:

Theoretical capacity Practical capacity Normal capacity

Master$-$budget capacity Required

$850,000$ bulbs $425,000$ bulbs

$272,000$ bulbs $($average expected output for the next $3$ years$)212,500$ bulbs expected production this year

$1.$ Calculate the inventoriable cost per unit using each level of capacity to compute fixed manufacturing cost per unit.

$2.$ Suppose EGL actually produces $250,000$ bulbs. Calculate the production$-$volume variance using each level of capacity to compute the fixed manufacturing overhead allocation rate.

$3.$ Assume EGL has no beginning inventory. If this year$$s actual sales are $212,500$ bulbs $($and production is $250,000$ bulbs$),$ calculate operating income for EGL using each type of capacity to compute fixed manufacturing cost per unit.

I need help with part $3$ and how to compute the gross margin, the fixed selling price$($breakeven$)$ and operating income. there are other solutions but please explain these parts with working notes.