WEEK TWO Edgerron Company is able to produce two products, G and B, with the sam
ID: 3261147 • Letter: W
Question
WEEK TWO
Edgerron Company is able to produce two products, G and B, with the same machine in its factory. The following information is available.
Product G
Product B
Selling price per unit
$
150
$
180
Variable costs per unit
60
108
Contribution margin per unit
$
90
$
72
Machine hours to produce 1 unit
0.4
hours
1.0
hours
Maximum unit sales per month
550
units
200
units
The company presently operates the machine for a single eight-hour shift for 22 working days each month. Management is thinking about operating the machine for two shifts, which will increase its productivity by another eight hours per day for 22 days per month. This change would require $9,000 additional fixed costs per month. (Round hours per unit answers to 1 decimal place. Enter operating losses, if any, as negative values.)
1. Determine the contribution margin per machine hour that each product generates.
Product G
Product B
Contribution margin per unit
$90.00
$72.00
Machine hours per unit
0.4
1.0
Contribution margin per machine hour
$72.00
Product G
Product B
Total
Maximum number of units to be sold
550
200
Hours required to produce maximum units
220
200
420
2. How many units of Product G and Product B should the company produce if it continues to operate with only one shift? How much total contribution margin does this mix produce each month?
Product G
Product B
Total
Hours dedicated to the production of each product
176
0
176
Units produced for most profitable sales mix
440
0
Contribution margin per unit
$0.00
Total contribution margin - one shift
3. If the company adds another shift, how many units of Product G and Product B should it produce? How much total contribution margin would this mix produce each month?
Product G
Product B
Total
Hours dedicated to the production of each product
220
132
352
Units produced for most profitable sales mix
550
132
Contribution margin per unit
$90.00
$72.00
Total contribution margin - two shifts
$49,500
$9,504
Yes
4. Suppose that the company determines that it can increase Product G’s maximum sales to 600 units per month by spending $8000 per month in marketing efforts. Should the company pursue this strategy and the double shift?
Product G
Product B
Total
Hours dedicated to the production of each product
240
112
352
Units produced for most profitable sales mix
600
112
Contribution margin per unit
$90.00
$72.00
Total contribution margin - two shifts and marketing campaign
$54,000
$8,064
No
Edgerron Company is able to produce two products, G and B, with the same machine in its factory. The following information is available.
Explanation / Answer
Q1
Contribution margin per machine hour that each product generates
Product G
Contribution margin per unit = $90
Machine hour per unit = 0.4
Contribution margin per machine hour = 90/0.4 = $225 ANSWER 1
Product B
Contribution margin per unit = $72
Machine hour per unit = 1
Contribution margin per machine hour = 72/1 = $72 ANSWER 2
Q2
Let x = number of units of Product G to be produced and y = number of units of Product B.
Then, total number of machine hours required = 0.4x + y and this should be less than or equal to maximum machine hours available, which is = 22 x 8 = 176.
So, we have: 0.4x + y 176 …………………………………………………..(1)
Similarly, considering the maximum sales possible per month, we have
x 550 and y 200…………………………………………………………..(2)
Total contribution per month at the above product mix: z = 90x + 72y ……..(3)
We want to maximize z subject to (1) and (2).
Now, maximum x satisfying (1) is 440 (i.e., when y = 0) and maximum y satisfying (1) is 176 (i.e., when x = 0). So, both satisfy (2). Hence, optimum decision would be to produce only either B or G depending on which yields higher total contribution.
At x = 440, from (3), z = 39600 and at y = 176, from (3), z = 12672.
Since 39600 > 12672, optimum decision is:
produce 440 units of Product G only. ANSWER 1 and then the corresponding
total monthly contribution = $39600 ANSWER 2
Q3
When 2 shifts are operated, available machine house becomes 352 and total contribution would come down by $9000, being the extra fixed cost incurred for additional shift. Thus, we have: maximize
z = 90x + 72y - 9000………………………………………….(4)
Subject to 0.4x + y 352 ………………………………………………………(5)
and x 550 and y 200…………………………………………………………..(6)
By graphical method of solving a Linear Programming Problem, we find the following 4 feasible cases (the corner points)
Case #
x
y
Total monthly contribution
1
0
200
*1
2
380
200
39600
3
550
132
50004
4
550
0
*2
*1 and *2 are not evaluated since trivially, case (2) is better than case (1) and
case (3) is better than case (4) in terms of total contribution.
Since 50004 > 39600, optimum decision is:
produce 550 units of Product G and 132 units of Product B. ANSWER 1
and then the corresponding
total monthly contribution = $50004 ANSWER 2
Q4
In this case, we will have:
maximize z = (90x – 8000) + 72y - 9000………………………………………….(4)
Subject to 0.4x + y 352 ………………………………………………………(5)
and x 600 and y 200…………………………………………………………..(6)
By graphical method of solving an Linear Programming Problem, we find the following 4 feasible cases (the corner points)
Case #
x
y
Total monthly contribution
1
0
200
*1
2
380
200
31600
3
600
112
45064
4
600
0
*2
*1 and *2 are not evaluated since trivially, case (2) is better than case (1) and
case (3) is better than case (4) in terms of total contribution.
Since 45064 > 31600, optimum decision is:
produce 600 units of Product G and 112 units of Product B, and then the corresponding
total monthly contribution = $45064.
But, since 50004 > 45064, the right decision would be: NOT to pursue this strategy of enhancing maximum sales of Product G and the double shift. ANSWER
Case #
x
y
Total monthly contribution
1
0
200
*1
2
380
200
39600
3
550
132
50004
4
550
0
*2
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