I have been going over this problem for hours with nothing coming up right. A company maintains no inventories and this is the data on one of its products that it has collected. Direct materials standard (4lbs @$1/lb) which comes to $4/unit. Total direct materials cost variance-unfavorable $13750. Actual direct materials used 125000 lbs. actual finished units produced 25000 units.
I did (AQ) x(AP)=125000xAP (AQ) x(SP)=125000 x$1/lb=$125000. I know that the purchase price variance is $13750 so I took 13750/125000 and got $.11 =AP. I'm stuck on the usage variance. I know that the actual cost of the direct materials purchased and used during the period are the same but don't know if I'm supposed to divide the actual direct materials used by actual units produced and work that in with the direct material standard. I'm lost. Please help.

By definition, the usage variance is

The difference between the quantity that should have been used, vs. the quantity that actually was used;
with this diff then multiplied by the standard cost per unit.


You have all three ingredients for this recipe: In producing 25,000 finished units, they should have consumed 100,000 lbs. of direct material. Instead, they used up 125,000 lbs. And the direct material has a standard cost of $1 per lb.

After you've computed this usage variance, add it to the price variance (that you've already correctly computed at $13,750), to see if this squares with the total variance:

In producing 25K of finished units, they should have used 100K lbs. of material, at $1 per lb. Instead, they used 125K lbs. which cost $1.11 per pound. This overall difference is an unfavorable total variance of..

And so the usage variance you compute from the 'recipe' above, plus the 13,750 unfav price variance, should agree with the total unfav variance.

Give that a whirl.

Usage Variance, as pointed out by Arcsine, is $25,000 (unfavorable). Now since the total material cost variance is $13,750 (U), that means that $11,250 is the price variance and that would give actual price as $1.09.