LP Problem 1
A) Standard problem formula:
Max 0.2A+0.15B+0.1C
S.t.
0.3A+0.5B+0.4C <= 1800 (assembly hours) 0.1A+0.08B+0.12C <= 800 (inspection hours) 0.06A+0.04B+0.05C <= 700 (packing hours) A, B, C >= 0
B)
D) 6,000 units of product A should be produced per week and 0 units of each product B and C should be produced. This strategy will result in total profit of $1,200 per week.
LP Problem 2
Two products are made by blending three raw materials according to these specifications:
Material
Price/Pound
Product
1
2
3
A
10%
≥30%
≤80%
$12.00
B
≥30%
≥20%
≤60%
$15.00
Mat’l Avail
4000
6000
10,000
Mat’l Cost
$3.00
$2.00
$1.00
All manufacturing costs, other than material, are assumed to be $2.00 per pound regardless of the product or blend. Determine the blend to use for each product and the quantities of each to produce each week to obtain maximum profits.
LP Problem 3
A plant makes three products, A, B, and C. The following data describe the production planning problem:
Profit Minimum
per Weekly
Product Piece Requirements
Processing Time in Hours per Piece
Lathe Dept.
Milling Dept.
Grinding Dept.
Inspection Packing
A $20 100 pieces
0.2
0.5
0.1
0.02
0.05
B 18 180
0.1
….
0.3
0.02
0.06
C 21 75
0.3
0.07
0.1
0.02
0.05
Department Capacity in Hours per Week
160
80
80
40
40
For example, products A and C have to be processed through all five departments, while product B would not have to be processed through the milling department.
Determine the weekly production rate for each product that maximizes profit.
LP Problem 4
A manufacturer of fertilizer markets four mixes of lawn fertilizer: 6-8-6, 10-6-4, 12-5-8, 14-5-10. The numbers refer to the percentage by weight of nitrates, phosphates, and potash, respectively, in the product.
Manufacturing is a mixing process whereby the active ingredients are mixed in the proper proportions with inert ingredients, and the mix is then packaged and sold.
For the period being planned, the manufacturer has available 2300 tons of nitrates, 1400 tons of phosphates, and 1800 tons of potash. He has access to a very large supply of the inert ingredients, so that they will not constrain his choice of a production program.
Demand data for the period are shown in the following table:
The company must produce at least the minimum quantity forecast and will not produce an amount greater than the maximum forecast.
The costs per ton of the fertilizer components are the following: nitrates, $200; phosphates, $60; potash, $90; other ingredients, $15. Costs of packaging materials, mixing, bagging, and selling are estimated to be $20 per ton, regardless of the mix.
Determine how much of each product to produce to maximize profit.
LP Problem 5
A company has three plants, all of which make the same product. This product is made to order and the decision problem is to determine at which plant an order should be made. The following orders are to be scheduled into production.
Customer
Order Size
Shipping Costs per Unit
From Plant 1
From Plant 2
From Plant 3
W
X
Y
Z
700 units
1500
400
500
$ 8.00
11.00
6.00
9.00
$ 4.00
10.00
12.00
5.00
$ 6.00
8.00
7.00
14.00
The production costs vary from plant to plant and so does the available capacity:
Plant
Unit Mfg. Cost
Capacity
A
$45
1000
B
$40
800
C
$50
1500
Find the minimum-cost production-distribution schedule, assuming that orders can be split among the plants.
LP Problem 1
A)
Sta
ndard problem formula
:
Max 0.2A+0.15B+0.1C
S.t.
0.3A+0.5B+0.4C <= 1800 ( assembly hours) 0.1A+0.08B+0.12C <= 800 ( inspection hours) 0.06A+0.04B+0.05C <= 700 ( packing hours) A, B, C >=
0
B)
D)
6,000
units
of
product
A
should
be
produced
per
w
eek
and
0
units
of
each
pro
duct
B
and
C
sho
uld
be
produced
.
This
strategy
will
result
in
total
profit
of
$
1,200
per
week
.
LP Problem 1
A) Standard problem formula:
Max 0.2A+0.15B+0.1C
S.t.
0.3A+0.5B+0.4C <= 1800 (assembly hours) 0.1A+0.08B+0.12C <= 800 (inspection hours) 0.06A+0.04B+0.05C <= 700 (packing hours) A, B, C >= 0
B)
D) 6,000 units of product A should be produced per week and 0 units of each product B and C
should be produced. This strategy will result in total profit of $1,200 per week.
Delivering a high-quality product at a reasonable price is not enough anymore.
That’s why we have developed 5 beneficial guarantees that will make your experience with our service enjoyable, easy, and safe.
You have to be 100% sure of the quality of your product to give a money-back guarantee. This describes us perfectly. Make sure that this guarantee is totally transparent.
Read moreEach paper is composed from scratch, according to your instructions. It is then checked by our plagiarism-detection software. There is no gap where plagiarism could squeeze in.
Read moreThanks to our free revisions, there is no way for you to be unsatisfied. We will work on your paper until you are completely happy with the result.
Read moreYour email is safe, as we store it according to international data protection rules. Your bank details are secure, as we use only reliable payment systems.
Read moreBy sending us your money, you buy the service we provide. Check out our terms and conditions if you prefer business talks to be laid out in official language.
Read more