King Furniture Company produces a chair for which the standard specifies $6$ yards of material per unit. The standard price of one yard of material is $$10\mathrm{.}55.$ During the month, $8,000$ chairs were manufactured, using $50,500$ yards at a cost of $$10\mathrm{.}25.$

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