T Ellsworth Company has signed a contract that requires them to produce and sell $50,000$ units for $$8$ per unit. A regression model was run using $27$ observations to measure total costs as a function of units. It is as follows:

Total costs $=$ $$90,000+$ $$6$ per unit

The standard error of the estimate is $$4,000.$

Required:

a$.$ Calculate the following assuming certainty:

i$.$ Breakeven in units and dollars

ii$.$ ii$.$ Sales quantity needed to obtain an after$-$tax profit of $$24,000.$ Assume that a $40$ percent tax rate is used for only part ii$.$

iii. Sales in dollars needed to obtain a pretax profit equal to $10$ percent of sales.

b$.$ Calculate the following assuming uncertainty:

i$.$ What is the range of incomes that would be expected with $90$ percent confidence? ii$.$ What is the range of incomes that would be expected with $95$ percent confidence?