Air United, Inc. manufactures two products: missile range instruments and space pressure gauges. During April, 49 range instruments and 297 pressure gauges were produced, and overhead costs of $88,560 were estimated. An analysis of estimated overhead costs reveals the following activities.
Activities

Cost Drivers

Total Cost

1. Materials handling Number of requisitions
$38,850

2. Machine setups Number of setups
26,190

3. Quality inspections Number of inspections
23,520

$88,560

The cost driver volume for each product was as follows.
Cost Drivers

Instruments

Gauges

Total

Number of requisitions 420 630 1,050
Number of setups 225 260 485
Number of inspections 265 225 490
Air United, Inc. manufactures two products: missil

Air United, Inc. manufactures two products: missil
Determine the overhead rate for each activity.
Overhead Rate

Materials handling $

Machine setups $

Quality inspections $

Air United, Inc. manufactures two products: missil

Air United, Inc. manufactures two products: missil
Assign the manufacturing overhead costs for April to the two products using activity-based costing. (Round per unit answers to 2 decimal places, e. g. 12.25.)
Instruments

Gauges

Total cost assigned $

$

Overhead cost per Unit $

$

Overhead Rate:

Materials handling = $ 37

Machine setups = $ 54

Quality inspections = $48

                                                  Instruments                Gauges

Total Cost Assigned $                  40,410                       48,150

Overhead Cost per Unit $            824.69                      162.12

Step-by-step explanation:

The overhead rate for each activity can be calculated by dividing the estimated overhead cost by the total number of cost drivers.

Material Handling:

Total Cost = $38,850

Cost Driver = Number of Requisitions = 1050

Overhead Rate = 38850/1050 = $37

Machine Setups:

Total Cost = $26,190

Cost Driver = No. of setups = 485

Overhead Rate = 26190/485 = $54

Quality Inspections:

Total Cost = $23520

Cost Driver = No. of inspections = 490

Overhead Rate = 23520/490 = $48

The total cost assigned for each of the products i.e. Instruments and Gauges can be calculated by multiplying the overhead costs with each of the cost drivers separately and then adding the costs to find the total cost.

Total Cost Assigned for Instruments:

Cost Assigned for Material Handling = No. of Instruments x Overhead Cost

                                                             = 420 x 37

Cost Assigned for Material Handling = $15,540

Cost Assigned for Machine Setups = No. of Instruments x Overhead Cost

                                                           = 225 x 54

Cost Assigned for Machine Setups = $12,150

Cost Assigned for Quality Inspections = No. of Instruments x Overhead Cost

                                                                = 265 x 48

Cost Assigned for Quality Inspections = $12,720

Total Cost Assigned for Instruments = $15,540 + $12,150 + $12,720

Total Cost Assigned for Instruments = $40,410

Overhead Cost Per Unit for Instruments = Total Cost Assigned/No. of Instruments Produced

                                                                   = $40,410/49

Overhead Cost Per Unit for Instruments = $824.69

Similarly, we will calculate the total cost assigned and the overhead cost per unit for gauges produced in April.

Total Cost Assigned for Gauges:

Cost Assigned for Material Handling = No. of Gauges x Overhead Cost

                                                             = 630 x 37

Cost Assigned for Material Handling = $23,310

Cost Assigned for Machine Setups = No. of Gauges x Overhead Cost

                                                           = 260 x 54

Cost Assigned for Machine Setups = $14,040

Cost Assigned for Quality Inspections = No. of Gauges x Overhead Cost

                                                                = 225 x 48

Cost Assigned for Quality Inspections = $10,800

Total Cost Assigned for Gauges = $23,310 + $14,040 + $10,800

Total Cost Assigned for Gauges = $48,150

Overhead Cost Per Unit for Gauges = Total Cost Assigned/No. of Gauges Produced

                                                                   = $48,150/297

Overhead Cost Per Unit for Gauges = $162.12

thats not a system of equations, that is a solution

x =-.20752

step-by-step explanation:

4^(x+2)=12

4^(x+2)=12

take the log base 4 on each side

log 4 (4^(x+2) = log 4(12)

we know log b(a^y) = y log b (a)

(x+2) log 4(4) = log 4 (12)

x+2 = log 4 (12)

we know   logb c = loga c/loga b

we want to convert to base 10   so a = 10

by default, we do not write the 10   c = 4   and b = 10

log4 10 = log 12/log 4

log4 10 = log 12/ log 4

x+2 = log 12/ log 4

subtract 2 from each side

x +2 -2 = log 12/ log 4 -2

x = 1.79248125 -2

x =-.20752