Question
Linear Programming (Statistics)
1.
The Outdoor Furniture Corporation manufactures two products, benches and picnic
tables, for use in yards and parks. The firm has two main resources: its carpenters (labor
force) and a supply of redwood for use in the furniture. During the next production cycle,
1,800 hours of labor are available under a union agreement. The firm also has a stock of
3,750 feet of good quality redwood. Each bench that Outdoor Furniture produces requires
6 labor hours and 16 feet of redwood: each picnic table takes 15 labor hours and 25 feet
of redwood. Completed benches will yield a profit of $13 each, and tables will result in a
profit of $26 each. How many benches and tables should Outdoors Furniture produce to
obtain the largest possible profit? Use the graphical method to solve the problem.
2. The seasonal yield of olives in a Piraeus, Greece, and vineyard is greatly influenced by a
process of branch pruning. If Olive trees are pruned every two weeks, output is increased.
The pruning process, however, requires considerably more labor then permitting the olive
grow on their own and result in a smaller size olive. It also, though, permits olive trees to
be spaced closer together. They yield of 1 barrel of olives by pruning requires 6 hours of
labor and 3 acres of land. The production of a barrel of olives by the normal process
requires only 5 labor hours but takes 8 acres of land. An olive grower has 360 hours of
labor available and a total of 288 acres for growing. Because of the olive size difference,
a barrel of olives produced on pruned trees sells for $ 32, whereas a barrel of regular
olives has a market price of $ 40. The grower has determined that because of uncertain
demand, no more than 30 barrels of pruned olives should be produced.
Use the graphical method to find.
(a)The maximum possible profit.
(b)The best combination of barrels of pruned and regular olives.
(c)The number of acres that the olive grower should devote to each growing process.
Reminder this problem must be solved using Solver in Excel.
Thanks! I need this in Excel form can you send me an attachment to
5#
The Feed N Ship Ranch fattens cattle for local farmers and ships them to meat markets in Kansas
City and Omaha. The owners of the ranch seek to determine the amounts of cattle feed to buy so
that minimum nutritional standards are satisfied, and at the same time total feed cost are
minimized. The feed mix can be made up of three grains that contain the following ingredients
per pound of feed:
The cost per pound of stocks X, Y, and Z are $2, $4, and $2.50 respectively. The minimum
requirement per cow per month is 4 pounds of ingredient A, 5.5 pounds of ingredient B, 1 pound
of ingredient C, and 8 pounds of ingredient D.
Feed (OZ)
Ingredient
A
Stock X
3
Stock Y
Stock Z
2
4
B
2
3
1
C
1
0
2
D
6
8
4
The ranch faces one additional restriction: it can only obtain 700 pounds of stock Z per month
from the feed supplier regardless of its need. Because there are usually 100 cows at the Feed N
Ship Ranch at any given time, this means that no more than 7 pounds of stock Z can be counted
on for use in the feed of each cow per month.
A) Formulate this as an LP problem
B) Solve this problem using Excel Solver.
6
#
The Weinberger Electronics Corporation manufactures four highly technical products that it
supplies to aerospace firms that hold NASA contracts. Each of the products must pass through
the following departments before they are shipped: wiring, drilling, assembly and inspection.
The time requirement in hours for each unit produced and its corresponding profit value are
summarized in the following table:
1.
Department
Product
Wiring
Drilling
Assembly
Inspection
Unit profit
XJ201
0.4
0.5
0.3
0.6
12
XM897
0.7
1.2
4.8
1.2
15
TR29
1.8
2.5
1.2
0.5
16
BR788
1.2
3.6
2.2
0.8
14
The production available in each department each month, and the minimum monthly production
requirement to fulfill contracts, are as follows:
Department
Capacity
(hours)
Product
Minimum
Prod. Level
Wiring
18,000
XJ201
250
Drilling
20,000
XM897
200
Assembly
27,600
TR29
400
Inspection
15,000
BR788
500
The production manager has the responsibility of specifying production levels for each product
for the coming month. Help him by formulating (that is, setting up the constraints and objective
function) Weinberger’s problem using LP. What is the optimal solution? Use the Excel Solver to
solve the problem.
7#
Raptor Fuels produces three grades of gasoline – Regular, Premium, and Super. All of these are
produced by blending two types of crude oil – Crude A and Crude B. The two types of crude
contain specific ingredients which help in determining the octane rating of gasoline. The
important ingredients and the costs are contained in the table below:
Crude
A
Crude B
Cost per gallon
$0.85
$0.96
Ingredient 1
40%
52%
Other
Ingredients
60%
48%
In order to achieve the desired octane ratings, at least 42% of Regular gasoline should be
ingredient 1; at least 45% of Premium gasoline must be ingredient 1, and at least 48% of Super
gasoline should be Ingredient 1. Due to current contract commitments, Raptor fuels must
produce at least 25,000 gallons of regular, at least 18,000 gallons of premium, and at least 15,600
gallons of Super, formulate linear program that could be used to determine how much of Crude A
and Crude B should be used in each of the gasolines to meet the demands at the minimum cost.
What is the minimum cost? How much of Crude A and Crude B are used in each gallon of the
different types of gasoline? Formulate this problem as a Linear Program and use Solver to find
the answers.
