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  1. Choose one problem from the “LP Problems” File
  2. For      each problem:
    1. Write       the standard problem formulation
    2. Solve       the problem using Excel
    3. Analyze       the results
    4. Describe       a practical way of achieving more, if it was needed, along with your       rationale for that particular choice
    5. Document       2a-2d in a Microsoft Word file, showing all relevant detail

LP Problem 1

A) Standard problem formula:

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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:

MaterialPrice/Pound
Product
123
A10%≥30%≤80%$12.00
B≥30%≥20%≤60%$15.00
Mat’l Avail4000600010,000
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 Minimumper WeeklyProduct Piece RequirementsProcessing Time in Hours per Piece
Lathe Dept.Milling Dept.Grinding Dept.Inspection Packing
$20 100 pieces0.20.50.10.020.05
18 1800.1….0.30.020.06
21 750.30.070.10.020.05
Department Capacity in Hours per Week16080804040

For example, products and C have to be processed through all five departments, while product 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.

CustomerOrder SizeShipping Costs per Unit
From Plant 1From Plant 2From Plant 3
WXYZ700 units1500400500$ 8.0011.006.009.00$ 4.0010.0012.005.00$ 6.008.007.0014.00

The production costs vary from plant to plant and so does the available capacity:

PlantUnit Mfg. CostCapacity
A$451000
B$40800
C$501500

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.

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