Standard Costing and Variance Analysis

Aiyanna Swartz Manufacturing, Inc. planned to produce $25,000$ units of a product during $2024.$

The Standard Cost data for the product is as follows:

DM $(3$lb @ $$2$ per pound$).....................................$$$6$ Per unit

DM $(0\mathrm{.}5$ hr @ $$8\mathrm{.}00$ per hour$)...............................$$$4$ Per unit

Variable overhead $(\mathrm{.}5$hr @ $$4\mathrm{.}00$ per hour$).........$$$2$ Per unit

The actual production was $24,000$ units, with the following actual total costs incurred:

DM $(74,000$ lb$.$ @ $$1\mathrm{.}80).........................................$$$133,200$ Total Cost

DL $(13,000$ hr$.$ @ $8\mathrm{.}10)..............................................$$$105,300$ Total Cost

Variable overhead......................................................$$50,200$ Total Cost

A$.$ Calculate the variances for materials, labor, and variable overhead

B$.$ Is the difference between the total actual cost and total standard cost equal to the sum

of all the variances? Why?