You said that S = 2(lw + lh + wh)
Divide each side by 2 : S/2 = lw + lh + wh
Subtract 'lh' from each side: S/2 - lh = lw + wh
Factor the right side: S/2 - lh = w(l + h)
Divide each side by (l + h) : (S/2 - lh) / (l + h) = w
Direct material cost variance = (Standard price - Actual Price) * Actual Quantity
= ($50 - $51) * 47,000
= $47,000 adverse
The answer is b many people want this product and havent purchased it yet