Question $1$

Door Knobs Inc, a producer of door knobs, expects that demand will increase markedly over the next decade. Due to the high fixed costs involved in the business, DKI 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 $$4\mathrm{.}50$ per door knob. Fixed manufacturing costs are $$2,000,000$ per year. Variable and fixed selling and administrative expenses are $$1\mathrm{.}50$ per door knob sold and $$450,000,$ respectively. DKI$$s door knobs are popular with mass$-$scale developers who buy their door knobs in bulk and DKI can sell its door knobs for $$15$ each. DKI is deciding whether to use, when calculating the cost of each unit produced:

Theoretical capacity $800,000$ door knobs

Practical capacity $500,000$ door knobs

Normal capacity $250,000$ door knobs $($average production for the next three years$)$

Master$-$budget capacity $200,000$ door knobs produced this year

Required:

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

b$)$ Calculate the production$-$volume variance using each level of capacity to compute the fixed manufacturing overhead allocation rate and this year$$s production of $230,000$ units.