Example of marginal costing and absorption costing

Gloom Co budgeted to make and sell $10,000$ units of its product in $2023.$ The selling price is $$10$ per unit and the variable cost $$4$ per unit. Fixed production costs were budgeted at $$50,000$ for the year. The company uses absorption costing and budgeted an absorption rate of $$5$ per unit. During $2023,$ it became apparent that sales demand would only be $8,000$ units. The management, concerned about the apparent effect of the low volume of sales on profits, decided to increase production for the year to $15,000$ units.

Actual fixed costs were still expected to be $$50,000$ in spite of the significant increase in production volume.

Required:

Calculate the profit at an actual sales volume of $8,000$ units, using the following methods.

$($a$)$ Absorption costing

$($b$)$ Marginal costing

Explain the difference in profits calculated.