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Appleby Manufacturing Uses an Activity-Based Costing System The Following Overhead Costs Are Reported for the Following Activities

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Appleby Manufacturing uses an activity-based costing system. The company produces Model F and Model G. Information relating to the two products is as follows:  Model F Model G Units produced 24,00030,000 Machine hours 7,5008,500 Direct labor hours 8,00012,000 Material handling (number of moves)  4,0006,000 Setups 5,0007,000 Purchase orders 3040 Inspections 10,00014,000 Product line variations 812\begin{array} { l r r } & \text { Model } \mathrm { F } & \text { Model } \mathrm { G } \\\text { Units produced } & 24,000 & 30,000 \\\text { Machine hours } & 7,500 & 8,500 \\\text { Direct labor hours } & 8,000 & 12,000 \\\text { Material handling (number of moves) } & 4,000 & 6,000 \\\text { Setups } & 5,000 & 7,000 \\\text { Purchase orders } & 30 & 40 \\\text { Inspections } & 10,000 & 14,000 \\\text { Product line variations } & 8 & 12\end{array} The following overhead costs are reported for the following activities of the production process:  Material handling $40,000 Labor-related overhead 120,000 Setups 60,000 Product design 100,000 Batch inspections 120,000 Central purchasing 70,000\begin{array} { l r } \text { Material handling } & \$ 40,000 \\\text { Labor-related overhead } & 120,000 \\\text { Setups } & 60,000 \\\text { Product design } & 100,000 \\\text { Batch inspections } & 120,000 \\\text { Central purchasing } & 70,000\end{array}
Jones manufacturing has used activity based costing to assign costs to Models F and G as given in the table below:  Activity  Cost Pool  Driver  Pool  Rate  Model F  Activity  Model F  Cost  Model G  Activity  Model G  Cost  Total  Material  handling $40,00010,000$44,000$16,0006,000$24,000$40,000 Labor related $120,00020,000$68,000$48,00012,000$72,000$120,000 overhead  Setups $60,00012,000$55,000$25,0007,000$35,000$60,000 Product  design $100,00020$5,0008$40,00012$60,000$100,000 Batch  Inspections $120,00024,000$510,000$50,00014,000$70,000$120,000 Central  purchasing $70,00070$1,00030$30,00040$40,000$70,000 total $209,000$301,000$510,000\begin{array}{|l|c|l|c|c|c|c|c|c|}\hline\text { Activity } & \text { Cost Pool } & \text { Driver } & \begin{array}{c}\text { Pool } \\\text { Rate }\end{array} & \begin{array}{c}\text { Model F } \\\text { Activity }\end{array} & \begin{array}{c}\text { Model F } \\\text { Cost }\end{array} & \begin{array}{c}\text { Model G } \\\text { Activity }\end{array} & \begin{array}{c}\text { Model G } \\\text { Cost }\end{array} & \text { Total } \\\hline \begin{array}{l}\text { Material } \\\text { handling }\end{array} & \$ 40,000 & 10,000 & \$ 4 & 4,000 & \$ 16,000 & 6,000 & \$ 24,000 & \$ 40,000 \\\hline \text { Labor related } & \$ 120,000 & 20,000 & \$ 6 & 8,000 & \$ 48,000 & 12,000 & \$ 72,000 & \$ 120,000 \\\text { overhead }\\\hline \text { Setups } & \$ 60,000 & 12,000 & \$ 5 & 5,000 & \$ 25,000 & 7,000 & \$ 35,000 & \$ 60,000 \\\hline \begin{array}{l}\text { Product } \\\text { design }\end{array} & \$ 100,000 & 20 & \$ 5,000 & 8 & \$ 40,000 & 12 & \$ 60,000 & \$ 100,000 \\\hline \begin{array}{l} \text { Batch }\\\text { Inspections }\end{array} & \$ 120,000 & 24,000 & \$ 5 & 10,000 & \$ 50,000 & 14,000 & \$ 70,000 & \$ 120,000 \\\hline \begin{array}{l} \text { Central }\\\text { purchasing }\end{array} & \$ 70,000 & 70 & \$ 1,000 & 30 & \$ 30,000 & 40 & \$ 40,000 & \$ 70,000 \\\hline\text { total }&&&&&\$209,000&&\$301,000&\$510,000\\\hline\end{array}
Appleby Manufacturing wants to implement an approximately relevant ABC system by using the two most expensive activities for cost assignment.
Under this new approach using consumption ratios for labor related and batch inspections, what set of equations would be used to create equally accurate reduced ABC allocation rates (where a = labor hours and b = batch inspections) ? (round to 5 decimal places)


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