Question
In: Statistics and Probability
Prime Co. produces two products, A and B. The unit revenues are $2 and $3, respectively....
Prime Co. produces two products, A and B. The unit
revenues are $2 and $3, respectively. Two
raw materials, M1 and M2, used in the manufacture of the two
products have daily availabilities
of 8 and 18 units, respectively. One unit of A uses 2 units of M1
and 2 units of M2, while one
unit of B uses 3 units of M1 and 6 units of M2.
(a) Using simplex method, determine the dual prices of M1 and M2
and their feasibility ranges.
(b) Suppose that 2 additional units of M1 can be acquired at the
cost of 25 cents per unit.
Would you recommend the additional purchase? Justify your
answer.
(c) Due to a change in people’s preferences, the unit revenue of A
changes to $(2 + ?).
Determine the optimality range for ? so that the optimum solution
stays the same.
show the steps please
Solutions
orchestra answered 1 year agoRelated Solutions
2.) A company manufactures two types of products, A and B. The unit revenues are $2...
2.) A company manufactures two types of products, A and B. The
unit revenues are $2 and $3, respectively. Two raw materials M1 and
M2, used in the manufacture of the two products have daily
availabilities of 4 and 6 units, respectively. One unit of A uses 1
unit of M1 and 1 unit of M2, and one unit of B uses 1 unit of M1
and 2 units of M2.
a) Formulate a linear programming model and obtain the...
Friendly Co. produces two products, A and B. The sales volume for A is at least...
Friendly Co. produces two products, A and B. The sales
volume for A is at least 80% of the total
sales of both A and B. However, the company cannot sell more than
110 units of A per day. Both
products use one raw material, of which the maximum daily
availability is 300 kg. The usage
rates of the raw material are 2 kg per unit of A, and 4 kg per unit
of B. The profit units for A...
JOBCO produces two products on two machines. A unit of product 1 requires 2 hours on...
JOBCO produces two products on two machines. A unit of product 1
requires 2 hours on machine 1 and 1 hour on machine 2. For product
2, a unit requires 1 hour on machine 1 and 3 hours on machine 2.
The revenues per unit of products 1 and 2 are $30 and $20,
respectively. The total daily processing time available for each
machine is 8 hours. Letting x1 and x2 represent the daily number of
units of products 1...
Henna Co. produces and sells two products, T and O. It manufactures these products in separate...
Henna Co. produces and sells two products, T and O. It
manufactures these products in separate factories and markets them
through different channels. They have no shared costs. This year,
the company sold 43,000 units of each product. Sales and costs for
each product follow.
Product T
Product O
Sales
$
761,100
$
761,100
Variable costs
608,880
76,110
Contribution margin
152,220
684,990
Fixed costs
33,220
565,990
Income before taxes
119,000
119,000
Income taxes (30% rate)
35,700
35,700
Net income
$...
Letter Co. produces and sells two products, T and O. It manufactures these products in separate...
Letter Co. produces and sells two products, T and O. It
manufactures these products in separate factories and markets them
through different channels. They have no shared costs. This year,
the company sold 48,000 units of each product. Sales and costs for
each product follow.
Product T
Product O
Sales
$
825,600
$
825,600
Variable costs
577,920
165,120
Contribution margin
247,680
660,480
Fixed costs
113,680
526,480
Profit before taxes
134,000
134,000
Income taxes (32% rate)
42,880
42,880
Net
profit
$...
Letter Co. produces and sells two products, T and O. It manufactures these products in separate...
Letter Co. produces and sells two products, T and O. It
manufactures these products in separate factories and markets them
through different channels. They have no shared costs. This year,
the company sold 53,000 units of each product. Sales and costs for
each product follow.
Product T
Product O
Sales
$
863,900
$
863,900
Variable costs
604,730
86,390
Contribution margin
259,170
777,510
Fixed costs
116,170
634,510
Profit before taxes
143,000
143,000
Income taxes (40% rate)
57,200
57,200
Net
profit
$...
Letter Co. produces and sells two products, T and O. It manufactures these products in separate...
Letter Co. produces and sells two products, T and O. It
manufactures these products in separate factories and markets them
through different channels. They have no shared costs. This year,
the company sold 53,000 units of each product. Sales and costs for
each product follow.
Product T
Product O
Sales
$
863,900
$
863,900
Variable costs
604,730
86,390
Contribution margin
259,170
777,510
Fixed costs
116,170
634,510
Profit before taxes
143,000
143,000
Income taxes (40% rate)
57,200
57,200
Net
profit
$...
Letter Co. produces and sells two products, T and O. It manufactures these products in separate...
Letter Co. produces and sells two products, T and O. It
manufactures these products in separate factories and markets them
through different channels. They have no shared costs. This year,
the company sold 48,000 units of each product. Sales and costs for
each product follow.
Product T
Product O
Sales
$
825,600
$
825,600
Variable costs
577,920
165,120
Contribution margin
247,680
660,480
Fixed costs
113,680
526,480
Profit before taxes
134,000
134,000
Income taxes (32% rate)
42,880
42,880
Net
profit
$...
Henna Co. produces and sells two products, T and O. It manufactures these products in separate...
Henna Co. produces and sells two products, T and O. It
manufactures these products in separate factories and markets them
through different channels. They have no shared costs. This year,
the company sold 58,000 units of each product. Sales and costs for
each product follow.
Product T
Product O
Sales
$
974,400
$
974,400
Variable costs
779,520
194,880
Contribution margin
194,880
779,520
Fixed costs
46,880
631,520
Income before taxes
148,000
148,000
Income taxes (32% rate)
47,360
47,360
Net income
$...
Benoit Company produces three products—A, B, and C. Data concerning the three products follow (per unit):...
Benoit Company produces three products—A, B, and C. Data
concerning the three products follow (per unit):
Product
A
B
C
Selling price
$
84.00
$
70.00
$
74.00
Variable expenses:
Direct materials
25.20
21.00
9.00
Other variable expenses
25.20
31.50
42.80
Total variable expenses
50.40
52.50
51.80
Contribution margin
$
33.60
$
17.50
$
22.20
Contribution margin ratio
40
%
25
%
30
%
The company estimates that it can sell 750 units of each product
per month. The same...
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