1 4. David Company produces two types of gears, Gear A and Gear B, with unit con
ID: 2442033 • Letter: 1
Question
14. David Company produces two types of gears, Gear A and Gear B, with unit contribution margins of $6 and $8, respectively. Each gear must spend time on a special machine. The firm owns five machines that together provide 12,000 hours of machine time per year. Gear A requires 12 minutes of machine time; Gear B requires 24 minutes of machine time.
A. What is the contribution margin per hour of machine time for Gear A? Gear B?
B. If David faces only the production constraint (12,000 hours of machine time), how many units of Gear A should be produced? Gear B? What is the total contribution margin from this product mix?
C. Now suppose that David cannot sell more than 45,000 units of each type of gear. How many units of Gear A should be produced? Gear B? What is the total contribution margin from this product mix?
Figure 13-6.
Present value of $1
Periods
4%
6%
8%
10%
12%
14%
1
0.962
0.943
0.926
0.909
0.893
0.877
2
0.925
0.890
0.857
0.826
0.797
0.769
3
0.889
0.840
0.794
0.751
0.712
0.675
4
0.855
0.792
0.735
0.683
0.636
0.592
5
0.822
0.747
0.681
0.621
0.567
0.519
6
0.790
0.705
0.630
0.564
0.507
0.456
7
0.760
0.665
0.583
0.513
0.452
0.400
8
0.731
0.627
0.540
0.467
0.404
0.351
9
0.703
0.592
0.500
0.424
0.361
0.308
10
0.676
0.558
0.463
0.386
0.322
0.270
Present value of an Annuity of $1
Periods
4%
6%
8%
10%
12%
14%
1
0.962
0.943
0.926
0.909
0.893
0.877
2
1.886
1.833
1.783
1.736
1.690
1.647
3
2.775
2.673
2.577
2.487
2.402
2.322
4
3.630
3.465
3.312
3.170
3.037
2.914
5
4.452
4.212
3.993
3.791
3.605
3.433
6
5.242
4.917
4.623
4.355
4.111
3.889
7
6.002
5.582
5.206
4.868
4.564
4.288
8
6.733
6.210
5.747
5.335
4.968
4.639
9
7.435
6.802
6.247
5.759
5.328
4.946
10
8.111
7.360
6.710
6.145
5.650
5.216
Periods
4%
6%
8%
10%
12%
14%
1
0.962
0.943
0.926
0.909
0.893
0.877
2
0.925
0.890
0.857
0.826
0.797
0.769
3
0.889
0.840
0.794
0.751
0.712
0.675
4
0.855
0.792
0.735
0.683
0.636
0.592
5
0.822
0.747
0.681
0.621
0.567
0.519
6
0.790
0.705
0.630
0.564
0.507
0.456
7
0.760
0.665
0.583
0.513
0.452
0.400
8
0.731
0.627
0.540
0.467
0.404
0.351
9
0.703
0.592
0.500
0.424
0.361
0.308
10
0.676
0.558
0.463
0.386
0.322
0.270
Explanation / Answer
A. What is the contribution margin per hour of machine time for Gear A? Gear B?
Gear A Gear B
Unit contribution margin $6 $8
Machine time required 12 minutes 24 minutes
Contribution margin per hour $30 $20
B. If David faces only the production constraint (12,000 hours of machine time), how many units of Gear A should be produced? Gear B? What is the total contribution margin from this product mix?
12,000 machine hours / 0.2 hours = 60,000 units of Gear A
Total contribution margin = 60,000 x $6 = $360,000
C. Now suppose that David cannot sell more than 45,000 units of each type of gear. How many units of Gear A should be produced? Gear B? What is the total contribution margin from this product mix?
Gear A Contribution 45,000 units x 0.2 x $30 = $270,000
Gear B Contribution 7,500 units x 0.4 x $20 = $60,600
Total Contribution margin $330,000
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