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The required answer is materials price variance=[tex]\$ 3,000 \mathrm{~F}$[/tex]
Materials quantity variance [tex]$=\$ 2,375 \mathrm{U}$[/tex]
Materials price variance:
When the actual price paid for materials used in manufacturing differs from the standard price for the materials, this is referred to as a material price variation (MPV). If the actual price paid for the materials is less than the standard price, the material price variance will be beneficial.
The materials quantity variance is calculated simply for the amount of materials utilized in production, as opposed to the materials price variance, which is computed for the total amount of materials purchased in the solution below.
Actual Quantity of Input, at Actual Price
[tex]$(\mathrm{AQ} \times \mathrm{AP})$ \\[/tex]= [tex]$20.000$[/tex] pounds [tex]$\times$ \\[/tex] [tex]$\$ 2.35$[/tex] per pound[tex]$=\$ 47,000$[/tex]
Actual Quantity of Input, at Standard Price
[tex]$(\mathrm{AQ} \times \mathrm{SP})$[/tex]= [tex]$20.000$[/tex] pounds [tex]$\times$[/tex] [tex]$\$ 2.50$[/tex] per pound [tex]$=\$ 50,000$[/tex]
Standard Quantity Allowed for Output, at Standard Price
[tex](\mathrm{SQ} \times \mathrm{SP}) \\[/tex]= [tex]13,800[/tex] pounds[tex]* } \times[/tex] [tex]\$ 2.50 \text { per pound } \\[/tex] [tex]=\$ 34,500[/tex]
Price Variance [tex]\$ 3,000 \mathrm{~F}=[/tex] [tex]14,750 \text { pounds } \times \$ 2.50 \text { per pound }=\$ 36,875[/tex]
Quantity Variance U= [tex]\$2,375[/tex]
[tex]$\star 3,000$[/tex] units [tex]$\times 4.6$[/tex] pounds per unit $=13,800$ pounds
Alternatively, the variances can be computed using the formulas:
Materials price variance [tex]$=\mathrm{AQ}(\mathrm{AP}-\mathrm{SP})$[/tex]
20,000 pounds [tex]$(\$ 2.35$[/tex] per pound [tex]$-\$ 2.50$[/tex] per pound [tex]$)=\$ 3,000 \mathrm{~F}$[/tex]
Materials quantity variance [tex]$=S P(A Q-S Q)$[/tex]
[tex]$\$ 2.50$[/tex] per pound [tex]$(14,750$[/tex] pounds [tex]$-13,800$[/tex] pounds [tex]$)=\$ 2,375 \mathrm{U}$[/tex]
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