37. Manufacturing Two factories produce three different types of kitchen appliances. The following table sum- marizes the production capacity, the number of each type of appliance ordered, and the daily operating costs for the factories. How many days should each factory operate to fill the orders at minimum cost? Find the minimum cost.

Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter2: Introduction To Spreadsheet Modeling
Section: Chapter Questions
Problem 20P: Julie James is opening a lemonade stand. She believes the fixed cost per week of running the stand...
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#37 look at both pages and please explain all steps
SECTIC
0.6
Programming
Number
ar
Factory 2
20/day
10/day
70/day
$20,000
Factory 1
Ordered
0.
pair of style 891 takes 10 minutes to cut out and 20
minutes to assemble and finish. Each pair of style 917
takes 10 minutes to cut out and 30 minutes to assemble
and finish. The plant has enough workers to provide
at most 7500 minutes per day for cutting and at most
19,500 minutes per day for assembly and finishing. The
profit on each pair of style 891 is $18.00, and the profit
on each pair of style 917 is $22.50. How many pairs of
cach style should be produced per day to obtain maxi-
mum profit? Find the maximum daily profit.
33. Nutrition A privately owned lake contains two types
of game fish, bass and trout. The owner provides two
types of food, A and B, for these fish. Bass require 2
units of food A and 4 units of food B, and trout require
5 units of food A and 2 units of food B. If the owner has
800 units of each food, find the maximum number of
fish the lake can support.
Appliance 1
Appliance 2
Appliance 3
Daily cost
1600
ts manufactures
anits. Its profit
If unit. Next
by two limited
vailable next
s, and the
- be at most
"abor hours and
it requires 3
ind how many
oduced next
S.
Kep/08
10/day
20/day
$10,000
500
2000
38. Nutrition In a laboratory experiment, two separate
toods are given to experimental animals. Each food
contains essential ingredients, A and B, for which the
animals have a minimum requirement; each food also
has an ingredient C, which can be harmful to the ani-
mals. The following table summarizes this information.
43
maximum
Food 1
Food 2
Required
nation of
campaign.
t on televi-
ch 1-min-
candidate
3 units/g
Ingredient A
Ingredient B
Ingredient C
10 units/g
6 units/g 12 units/g
3 units/g
49 units
60 units
1 unit/g
34. Nutrition In a zoo, there is a natural habitat contain-
ing several feeding areas. One of these areas serves as
a feeding area for two species, I and II, and is supplied
cach day with 120 pounds of food A, 110 pounds of
food B, and 57 pounds of food C. Each individual of
species I requires 5 lb of A, 5 lb of B, and 2 lb of C, and
each individual of species II requires 6 lb of A, 4 lb of
B, and 3 lb of C. Find the maximum number of the two
species that can be supported.
Deople, and
advertise-
hould be
/minute
How many grams of foods 1 and 2 should be given to
the animals to satisfy the requirements for A and B
while minimizing the amount of ingredient C ingested?
39. Manufacturing The Janie Gioffre Drapery Company
makes three types of draperies at two different loca-
tions. At location I, it can make 10 pairs of deluxe
drapes, 20 pairs of better drapes, and 13 pairs of stan-
dard drapes per day. At location II, it can make 20 pairs
of deluxe, 50 pairs of better, and 6 pairs of standard per
day. The company has orders for 2000 pairs of deluxe
drapes, 4200 pairs of better drapes, and 1200 pairs of
standard drapes. If the daily costs are $500 per day at
location I and $800 per day at location II, how many
days should Janie schedule at each location to fill the
orders at minimum cost? Find the minimum cost.
be
-on their
equire
for
Shadow prices-land management For Problems 35 and
36, refer to the farm co-op application in Example 2(a).
Rework that linear programming problem with the indi-
cated changes in one constraint and answer the questions.
35. (a) If one more acre of land became available (for a
total of 6001 acres), how would this change the
co-op's planting strategy and its maximum profit?
(b) Repeat part (a) if 8 more acres of land were
available.
(c) Based on parts (a) and (b), what is the profit value
of each additional acre of land? This value is called
the shadow price of an acre of land.
36. (a) If one more gallon of fertilizer/herbicide became
available (for a total of 40,501 gallons), how would
this change the co-op's planting strategy and its
maximum profit?
(b) Repeat part (a) if 8 more gallons of fertilizer/herbi-
cide were available.
(c) Based on parts (a) and (b), what is the profit value
h additional gallon of fertilizer/herbicide
(that is, the shadow price of a gallon of fertilizer/
herbicide)?
ats for
ance
rizes
nd
any
co
40. Nutrition Two foods contain proteins, carbohydrates
and fats. Food A costs $1 per pound and contains 309
protein, 10% fat, and 50% carbohydrates. Food B cos
$1.50 per pound and contains 20% protein, 4% fat, a
75% carbohydrates. What combination of these two
do foods provides at least 1 pound of protein, 2 pounc
ocarbohydrates, and pound of fat at the lowest cost
41. Manufacturing A sausage company makes two di
oent kinds of hot dogs, regular and all beef. Each
of all-beef hot dogs requires 0.75 lb of beef and 0.
of spices, and each pound of regular hot dogs req
0.18 lb of beef, 0.3 lb of pork, and 0.2 lb of spices-
pliers can deliver at most 1020 lb of beef, at mos
of pork, and at least 500 lb of spices. If the profi
$1.50 on each pound of all-beef hot dogs and $
each pound of regular hot dogs, how many pou
each should be produced to obtain maximum
What is the maximum profit?
42. Manufacturing A cereal manufacturer mak
different kinds of cereal, Senior Citizen's Fea
Kids Go. Each pound of Senior Citizen's Fe:
1oods
nent
po
of eac
37. Manufacturing Two factories produce three different
types of kitchen appliances. The following table sum-
marizes the production capacity, the number of each
type of appliance ordered, and the daily operating costs
for the factories. How many days should each factory
operate to fill the orders at minimum cost? Find the
atbo
minimum cost.
Transcribed Image Text:SECTIC 0.6 Programming Number ar Factory 2 20/day 10/day 70/day $20,000 Factory 1 Ordered 0. pair of style 891 takes 10 minutes to cut out and 20 minutes to assemble and finish. Each pair of style 917 takes 10 minutes to cut out and 30 minutes to assemble and finish. The plant has enough workers to provide at most 7500 minutes per day for cutting and at most 19,500 minutes per day for assembly and finishing. The profit on each pair of style 891 is $18.00, and the profit on each pair of style 917 is $22.50. How many pairs of cach style should be produced per day to obtain maxi- mum profit? Find the maximum daily profit. 33. Nutrition A privately owned lake contains two types of game fish, bass and trout. The owner provides two types of food, A and B, for these fish. Bass require 2 units of food A and 4 units of food B, and trout require 5 units of food A and 2 units of food B. If the owner has 800 units of each food, find the maximum number of fish the lake can support. Appliance 1 Appliance 2 Appliance 3 Daily cost 1600 ts manufactures anits. Its profit If unit. Next by two limited vailable next s, and the - be at most "abor hours and it requires 3 ind how many oduced next S. Kep/08 10/day 20/day $10,000 500 2000 38. Nutrition In a laboratory experiment, two separate toods are given to experimental animals. Each food contains essential ingredients, A and B, for which the animals have a minimum requirement; each food also has an ingredient C, which can be harmful to the ani- mals. The following table summarizes this information. 43 maximum Food 1 Food 2 Required nation of campaign. t on televi- ch 1-min- candidate 3 units/g Ingredient A Ingredient B Ingredient C 10 units/g 6 units/g 12 units/g 3 units/g 49 units 60 units 1 unit/g 34. Nutrition In a zoo, there is a natural habitat contain- ing several feeding areas. One of these areas serves as a feeding area for two species, I and II, and is supplied cach day with 120 pounds of food A, 110 pounds of food B, and 57 pounds of food C. Each individual of species I requires 5 lb of A, 5 lb of B, and 2 lb of C, and each individual of species II requires 6 lb of A, 4 lb of B, and 3 lb of C. Find the maximum number of the two species that can be supported. Deople, and advertise- hould be /minute How many grams of foods 1 and 2 should be given to the animals to satisfy the requirements for A and B while minimizing the amount of ingredient C ingested? 39. Manufacturing The Janie Gioffre Drapery Company makes three types of draperies at two different loca- tions. At location I, it can make 10 pairs of deluxe drapes, 20 pairs of better drapes, and 13 pairs of stan- dard drapes per day. At location II, it can make 20 pairs of deluxe, 50 pairs of better, and 6 pairs of standard per day. The company has orders for 2000 pairs of deluxe drapes, 4200 pairs of better drapes, and 1200 pairs of standard drapes. If the daily costs are $500 per day at location I and $800 per day at location II, how many days should Janie schedule at each location to fill the orders at minimum cost? Find the minimum cost. be -on their equire for Shadow prices-land management For Problems 35 and 36, refer to the farm co-op application in Example 2(a). Rework that linear programming problem with the indi- cated changes in one constraint and answer the questions. 35. (a) If one more acre of land became available (for a total of 6001 acres), how would this change the co-op's planting strategy and its maximum profit? (b) Repeat part (a) if 8 more acres of land were available. (c) Based on parts (a) and (b), what is the profit value of each additional acre of land? This value is called the shadow price of an acre of land. 36. (a) If one more gallon of fertilizer/herbicide became available (for a total of 40,501 gallons), how would this change the co-op's planting strategy and its maximum profit? (b) Repeat part (a) if 8 more gallons of fertilizer/herbi- cide were available. (c) Based on parts (a) and (b), what is the profit value h additional gallon of fertilizer/herbicide (that is, the shadow price of a gallon of fertilizer/ herbicide)? ats for ance rizes nd any co 40. Nutrition Two foods contain proteins, carbohydrates and fats. Food A costs $1 per pound and contains 309 protein, 10% fat, and 50% carbohydrates. Food B cos $1.50 per pound and contains 20% protein, 4% fat, a 75% carbohydrates. What combination of these two do foods provides at least 1 pound of protein, 2 pounc ocarbohydrates, and pound of fat at the lowest cost 41. Manufacturing A sausage company makes two di oent kinds of hot dogs, regular and all beef. Each of all-beef hot dogs requires 0.75 lb of beef and 0. of spices, and each pound of regular hot dogs req 0.18 lb of beef, 0.3 lb of pork, and 0.2 lb of spices- pliers can deliver at most 1020 lb of beef, at mos of pork, and at least 500 lb of spices. If the profi $1.50 on each pound of all-beef hot dogs and $ each pound of regular hot dogs, how many pou each should be produced to obtain maximum What is the maximum profit? 42. Manufacturing A cereal manufacturer mak different kinds of cereal, Senior Citizen's Fea Kids Go. Each pound of Senior Citizen's Fe: 1oods nent po of eac 37. Manufacturing Two factories produce three different types of kitchen appliances. The following table sum- marizes the production capacity, the number of each type of appliance ordered, and the daily operating costs for the factories. How many days should each factory operate to fill the orders at minimum cost? Find the atbo minimum cost.
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