Need to have charts,formulas added, and reworded assignment converted into excel

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B1. Solve the following linear programming problem
graphically:
Maximize profit = 4X + 6Y
Subject to	X+2Y<8
	5X+4Y<20
	X,Y>0

Answer

X	Y	Maximize 4X  6Y
0	0	0
4	0	16
0	4	24
1.33	3.33	25.33 (optimal)

B5. Solve the following LP problem graphically:
Minimize cost = 24X + 15Y
Subject to:	7X+11Y>77
	16X +4Y>80
	X,Y>0

B.5

X	Y	Minimize 24X  15Y
0	20	300
11	0	264
3.86	4.54	160.86 (optimal)

B7.

The Attaran Corporation manufactures two electrical

products: portable air conditioners and portable heaters. The

assembly process for each is similar in that both require a certain

amount of wiring and drilling. Each air conditioner takes 3 hours

of wiring and 2 hours of drilling. Each heater must go through

2 hours of wiring and 1 hour of drilling. During the next production

period, 240 hours of wiring time are available and up to

140 hours of drilling time may be used. Each air conditioner sold

yields a profit of $25. Each heater assembled may be sold for a

$15 profit.

Formulate and solve this LP production-mix situation, and

find the best combination of air conditioners and heaters that

yields the highest profit.

ANSWER:

Let x1 number of air conditioners to be produced

x2 number of heaters to be produced

Maximize 25x1  15x2

Subject to 3x1  2x2 240 (wiring)

2x1  1x2 140 (drilling)

x1, x2 0 (non-negativity)

Profit:

@a: (x1  0, x2  0) Obj  $0

@b: (x1  0, x2  120) Obj  25  0  15  120  $1,800

@c: (x1  40, x2  60) Obj  25  40  15  60  $1,900*

@d: (x1  70, x2  0) Obj  25  70  15  0  $1,750

* The optimal solution is to produce 40 air conditioners and 60 heaters each period. Profit will be $1,900.

B11.

The Sweet Smell Fertilizer Company markets bags

of manure labeled “not less than 60 lb dry weight.” The packaged

manure is a combination of compost and sewage wastes. To

provide good-quality fertilizer, each bag should contain at least

30 lb of compost but no more than 40 lb of sewage. Each pound

of compost costs Sweet Smell 5¢ and each pound of sewage costs

4¢. Use a graphical LP method to determine the least-cost blend

of compost and sewage in each bag.

ANSWER

Let: X1  number of pounds of compost in each bag

X2  number of pounds of sewage waste in each bag

Minimize cost  5X1  4X2 (in cents)

Subject to X1  X2 60 (pounds per bag)

X1 30 (pounds compost per bag)

X2 40 (pounds sewage per bag)

Corner point a:

(X1  30, X2  40) cost  5(30)  (4)(40)  $3.10

Corner point b (which is optimal):

(X1  30, X2  30) cost  5(30)  (4)(30)  $2.70

Corner point c:

(X1  60, X2  0) cost  5(60)  (4)(0)  $3.00

B21. Par, Inc., produces a standard golf bag and a deluxe
golf bag on a weekly basis. Each golf bag requires time for cutting
and dyeing and time for sewing and finishing, as shown in the following
table:

PRODUCT	CUTTING & DYEING	SEWING & FINISHING
STANDARD BAG	0.50	1.00
DELUXE BAG	1.00	0.67


The profits per bag and weekly hours available for cutting and
dyeing and for sewing and finishing are as follows:

PRODUCT	PROFIT PER UNIT
STANDARD BAG	10.00
DELUXE BAG	8.00

ACTIVITY	WEEKLY HOURS AVAILABLE
CUTTING & DYEING	300.00
SEWING & FINISHING	360.00

Par, Inc., will sell whatever quantities it produces of these two
products.
a) Find the mix of standard and deluxe golf bags to produce per
week that maximizes weekly profit from these activities.
b) What is the value of the profit?

ANSWER

(a, b) Let S = number of standard bags to produce per week

D = number of deluxe bags to produce per week

Maximize profit = 10S + 8D

Extreme (Corner) Points

Point

Profit

(0, 0)

Macintosh HD:Users:dwsavage254:Library:Caches:TemporaryItems:msoclip:0:clip_image001.png

(0, 300)

$2,400

(360, 0)

$3,600

(240, 180)

$3,840

14.8

As the production planner for Scott Sampson

Products, Inc., you have been given a bill of material for a bracket

that is made up of a base, two springs, and four clamps. The base

is assembled from one clamp and two housings. Each clamp has

one handle and one casting. Each housing has two bearings and

one shaft. There is no inventory on hand.

a) Design a product structure noting the quantities for each item

and show the low-level coding.

b) Determine the gross quantities needed of each item if you are

to assemble 50 brackets.

c) Compute the net quantities needed if there are 25 of the base

and 100 of the clamp in stock

ANSWER:

14.8 (a)

(b) For 50 brackets, the gross requirements are for 50 bases, 100 springs, 250 clamps, 250 handles, 250 castings, 100 housings, 200 bearings, and 100 shafts.

(c) For 50 brackets net requirements are: 25 bases, 100 springs, 125 clamps, 125 handles, 125 castings, 50 housings, 100 bearings, and 50 shafts.

14.9

Your boss at Scott Sampson Products, Inc., has just
provided you with the schedule and lead times for the bracket in
Problem 14.8. The unit is to be prepared in week 10. The lead
times for the components are bracket (1 week), base (1 week),
spring (1 week), clamp (1 week), housing (2 weeks), handle
(1 week), casting (3 weeks), bearing (1 week), and shaft (1 week).

a) Prepare the time-phased product structure for the bracket.
b) In what week do you need to start the castings? ANSWER

(a) Time-phased product structure for bracket with start times:

FG14_009_0131585576

(b) Castings need to start in week 4.

+300 ()

360 ()

, 0

SDA

SDB

+£