Quantitative Analysis For Business
A creamery purchases three different types 951 pounds
of cheese: panela cheese at $3.75 per
pound, goat cheese at $7.10 per pound,
and Oaxaca cheese at $4.50 per pound.
The daily demand for each cheese is 45,
22, and 63 pounds respectively. The
creamery has a dedicated supplier for each
type of cheese, and the ordering cost is
$2.00 per order. It is expensive to keep
these products in inventory because
they are highly perishable. The holding
cost is estimated to be 0.5% of the
purchasing price for each type of
cheese.
A small manufacturer of mountain $112,800
bikes located in Denver, Colorado,
buys tires from a supplier in China. There
is a monthly demand of 200 tires. The cost
of placing an order is $200 and the
holding cost is $24 per tire per year. If
the purchasing price is
$45 per tire and the economic order
quantity is used, what is the total annual
inventory cost?
, A textile company produces tablecloths Min Z = 9.50X 1 + 3.50X 2
and cloth napkins. The production process
includes two steps: cutting and sewing.
Every day at least 2 production hours must
be worked in the cutting department and 6
production hours must be worked in the
sewing department. The time needed
for cutting and sewing each item as well as
the production costs for each item are
provided in the table below:
ProductTime Needed to Cut FabricTime
Needed to SewProduction
CostsTablecloths8 minutes9
minutes$9.50Cloth Napkins1.5 minutes6
minutes$3.50
Let X 1 represent the number of
tablecloths to be produced and let X 2
represent the number of cloth napkins
to be produced. What is the equation of
the objective function Z that optimizes
the production cost?
A manufacturing plant produces exactly 10 Min Z = 5 X 1 + 4 X 2 + 3 X 3Subject to X 1 + X 2 + X 3 = 1045 X 1 + 50 X 2 + 55 X 3 ≤ 480 X 1,
tons of a combination of three products per X 2, X 3 ≥ 0
day. The production costs are five, four,
and three dollars for products one, two,
and three, respectively. The plant works
480 minutes per day. Each ton of
product one, two, and three requires 45,
50, and 55 minutes of processing time,
respectively.
What is the correct linear programming
model for minimizing the production cost?
Consider the following linear programming 0
formulation: MIN
26X 1 + 14X 2 +12X 3
Subject to
2X 1+3X 2+1X 3≥30
6X 1+3X 2+1X
3≥50 X 1, X 2, X 3
≥0
The optimal solution is OBJECTIVE
FUNCTION VALUE 1) 228.0000 VARIABLE
VALUE REDUCED COST X1 5.000000
26.000000 X2 7.000000 14.000000 X3
0.000000 12.000000 ROW SLACK OR
SURPLUS DUAL PRICES 2) 1.000000
0.000000 3) 1.000000 0.000000 What is the
optimal value of X 3?
A sporting goods company makes The amount of material available
sports bandanas and flags. It costs $10 to
produce one bandana and $12 to
produce one flag. It takes 1/4 yard of
material to make one bandana and 1/2
yard of material to make one flag.What
is the constraint in this scenario?
A creamery purchases three different types 951 pounds
of cheese: panela cheese at $3.75 per
pound, goat cheese at $7.10 per pound,
and Oaxaca cheese at $4.50 per pound.
The daily demand for each cheese is 45,
22, and 63 pounds respectively. The
creamery has a dedicated supplier for each
type of cheese, and the ordering cost is
$2.00 per order. It is expensive to keep
these products in inventory because
they are highly perishable. The holding
cost is estimated to be 0.5% of the
purchasing price for each type of
cheese.
A small manufacturer of mountain $112,800
bikes located in Denver, Colorado,
buys tires from a supplier in China. There
is a monthly demand of 200 tires. The cost
of placing an order is $200 and the
holding cost is $24 per tire per year. If
the purchasing price is
$45 per tire and the economic order
quantity is used, what is the total annual
inventory cost?
, A textile company produces tablecloths Min Z = 9.50X 1 + 3.50X 2
and cloth napkins. The production process
includes two steps: cutting and sewing.
Every day at least 2 production hours must
be worked in the cutting department and 6
production hours must be worked in the
sewing department. The time needed
for cutting and sewing each item as well as
the production costs for each item are
provided in the table below:
ProductTime Needed to Cut FabricTime
Needed to SewProduction
CostsTablecloths8 minutes9
minutes$9.50Cloth Napkins1.5 minutes6
minutes$3.50
Let X 1 represent the number of
tablecloths to be produced and let X 2
represent the number of cloth napkins
to be produced. What is the equation of
the objective function Z that optimizes
the production cost?
A manufacturing plant produces exactly 10 Min Z = 5 X 1 + 4 X 2 + 3 X 3Subject to X 1 + X 2 + X 3 = 1045 X 1 + 50 X 2 + 55 X 3 ≤ 480 X 1,
tons of a combination of three products per X 2, X 3 ≥ 0
day. The production costs are five, four,
and three dollars for products one, two,
and three, respectively. The plant works
480 minutes per day. Each ton of
product one, two, and three requires 45,
50, and 55 minutes of processing time,
respectively.
What is the correct linear programming
model for minimizing the production cost?
Consider the following linear programming 0
formulation: MIN
26X 1 + 14X 2 +12X 3
Subject to
2X 1+3X 2+1X 3≥30
6X 1+3X 2+1X
3≥50 X 1, X 2, X 3
≥0
The optimal solution is OBJECTIVE
FUNCTION VALUE 1) 228.0000 VARIABLE
VALUE REDUCED COST X1 5.000000
26.000000 X2 7.000000 14.000000 X3
0.000000 12.000000 ROW SLACK OR
SURPLUS DUAL PRICES 2) 1.000000
0.000000 3) 1.000000 0.000000 What is the
optimal value of X 3?
A sporting goods company makes The amount of material available
sports bandanas and flags. It costs $10 to
produce one bandana and $12 to
produce one flag. It takes 1/4 yard of
material to make one bandana and 1/2
yard of material to make one flag.What
is the constraint in this scenario?
