Ruby Company produces a chair for which the standard specifies $5$ yards of material per unit. The standard price of one yard of material is $$7\mathrm{.}60.$ During the month, $8,500$ chairs were manufactured, using $40,000$ yards at a cost of $$7\mathrm{.}50.$

Determine the $($a$)$ direct materials price variance, $($b$)$ direct materials quantity variance, and $(c)$ total direct materials cost variance.