Answer:
First of all lets compute profit per unit as per existing data which is as below:
Selling price=$45/unit
Variable production cost=$25/unit
Labour cost=$12.5/unit ($25*50%)
Material cost=$6.25/unit($25*25%)
Variable overhead cost=$6.25/unit($25*25%)
Fixed cost=$11.47/unit ($780,000/68000 units)
Profit=$8.53 ($45-$25-$11.47)
Now lets calculate profit based on certain changes
Selling price=$49.5/unit ($45*10%)(As stated in question that assume maximum price increase)
Variable production cost=$30/unit ($15+$7.1875+$7.8125)
Labour cost=$15/unit ($12.5*1.2) (Labour cost to be increased by 20%)
Material cost=$7.1875/unit($6.25*1.15) (Material cost to be increased by 15%)
Variable overhead cost=$7.8125/unit($6.25*1.25) (V.POH to be increased by 25%)
Profit=$8.9545 ($8.53*1.05) (As stated in question profit must be increased by 5%)
Fixed cost=$819,000 ($780,000*1.05) (Fixed cost to be increased by 5%)
Fixed cost per unit=$10.5455 ($8.9545+$30-$49.5) Reverse working
Lets calculate volume by fixed cost per unit formula
Volume in units = Fixed cost/Fixed cost per unit
=$819,000/$10.5455
=77,663.5 units
Sales value = $695,438.27 (77,663.5*$8.9545)
