linear programming sheet

7/23/2019 Linear Programming Sheet

http://slidepdf.com/reader/full/linear-programming-sheet 1/3

Sheet (1)

Graphical Solution

1) A vehicle organization has two sorts of trucks, Type A and Type B.

Sort A has a refr igerated part of 2 !" and a non#refr igerated part of $

!" while Type B has the sa!e general volu!e with e%uivalent areas for

refr igerated and non#refr igerated s tock. A !erchant needs to contract

trucks for !oving of ", !" of refr igerated stock and $ !" of non#

refr igerated stock. The e&pense per ki lo!eter of a Type A is '", and '$

for Type B. (hat nu!er of trucks of every sort should the !erchant rent

to acco!plish !ini!u! e&pense* +, -,

$1/)

2) A co!pany is setting up a trip for $ e!ployees. The organization

handl ing t ransportation has 1 uses of seats each and / uses of $

seats, yet 0ust has drivers. The renta l of the ig us is '/ and '- for

the l i t t le us. alculate how !any uses of each type should e used for

the trip for the least possile cost. +$3arge, S!all, -2')

") A clothes factory needs to sel l inventory of 2 of i ts shir ts and

1 pairs of pants fro! last production. They have decided to put together

two offers , A and B. 4ffer A consists of one shir t and a pair of pants for

'". 4f fer B cons i s t s of three sh i r t s and a pa i r of pant s for '. Thefactory does not want to sel l less than 2 packages of 4ffer A and less

than 1 of 4ffer B. 5ow !any packages of each do they have to sel l to

!a&i!ize their sales outco!e*

+, , $')

$) A far!er has a l and he want s to p lant wi th corn and wheat . 5ecan far! up to / acres . 5e can earn ', for every acre he plants wi thwheat and '", for every acre he plants wi th corn. 5e can6 t use !oret ha n 1 g al lo ns o f p es ti ci de f or h is e nt ir e l an d. ( he at r e% u ir es 2

gal lons of pes t i c ide for every acre p lanted and corn re%ui res 1 ga l lon per acre. (hat is the !a&i!u! profi t he can !ake*+2/, ')

) An ar t i s t has "2 gra!s of ye l low color and $ gra!s of greencolor . 5e needs to !ake as !uch as poss ile of color A and color B for h i s ne&t a r twork . 7ach ucket of co lor A conta ins $ gra!s of ye l low



color and 1 g! of green dye . 7ach ucket of co lor B contains 1 g! of ye l l ow dye and - g r a!s o f g r een dye . 8 i nd t he !a& i !u! nu!er o f uckets he can !i&.

+-, /)

-) A 0 eweler se l l s cus to!ized 0 ewel ry for h i s cus to!ers a t the i r t a s t e . A cos t u!er wan t s t o des i gn he r own neck l ace f r o! whi t e and lack pearls . She wants to !ake a necklace at leas t 12 inches long, utno !ore t han 2$ i nches l ong . She a l so want s he r neck l ace t o cont ai n lack pearls that are at least twice the length of whi te pear ls . 8inally,she want s her necklace to have a t l eas t inches of lack pear l s . 8 indthe cons t ra in t s , ske tch the prole! and f ind the ver t i ces + in ter sec t ion points) .

) A far!er wants to prepare a new fer t i l izer wi th !ini!u! cos t y

!i&ing two fer t i li zer s, A and B. The !i&ture i s to conta in 9 a t l eas t $uni t s of phosphate , a t l eas t "- uni t s of n i t r a t e and a t l eas t $ uni t s of a!!oniu!. 8e rt i li zer A cos t s t he s hop ' . pe r pound . 8e rt i li zer Bc os ts t he sh op ' 1. / p er p ou nd . 8 er ti li ze r A c on ta in s u ni ts o f phosphate and 2 units of ni trate and 2 units of a!!oniu!. 8ert i l izer Bc o n t a i n s " u n i t s o f p h o s p h a t e a n d " u n i t s o f n i t r a t e a n d u n i t s o f a!!oniu!. 5ow !any pounds of each fer t i l izer should the shop use inorder to !ini!ize thei r cos t*

+1, 2)

/) A far!er needs to feed his sheep a daily n utritious !eal containinga !ini!u! of 2$ gra!s +g) of protein, "- g of carohydrates, and $ g of

fat . But the sheep should e fed no !ore than f ive ounces of food a day.

To prepare the !eal he lends certain a!ounts of product A and product

B. :roduct A contains / g of protein, 12 g of carohydrates, and 2 g of fat

per ounce, and costs '.2 per ounce. :roduct B contains 12 g of protein,

12 g of carohydrates , and 1 g of fat per ounce, at a cos t of '." per

ounce. (hat is the opti!al lend*

+", )

) An investor has '12, to invest, and three different invest!ents

to choose fro!. ;egular onds with a < return, special onds with an /<

return, and the stoc k !arket with 12< return. To !ini!ize risk, he decides

not to inves t any !ore than '2, in the s tock !arket . The ank rules

force hi! to invest at least three t i!es as !uch in the regular onds as in



the special onds. Assu!ing the year#end profi ts are as e&pected, what is

the !a&i!u! possile return* +- ')

1) An oil well produces at least two arrels of diesel fuel for each arrel of fuel oil. At least three !il lion arrels of fuel oil !ust e

produced daily. The de!and for diesel fuel is not !ore than -.$ !illion

arrels a day.

= f d ie se l i s s el li ng f or '1. per ar re l and f ue l o il s el ls f or

'1 .>arre l, what i s the !a&i!u! revenue possile* +1- .- ! ')

11) A ce llphone co!pany produces a r egular device and a s!ar t

!odel. Sales pro0ect ions e&pect sales of at least 1 regular and / s!art

devices daily. The factory capacity l i!its production to no !ore than 2

regular and 1 s!art devices daily. To satisfy a shipping contract, a total

of at least 2 devices !uch e shipped each day. =f each regular cell sold

results in a '2 loss, ut each s!art cell produces a ' profit, how !any of

each type should e !ade dai ly to !a&i!ize net prof i ts* +1 regular ,

1 s!art)

12) A lirary needs to u y so!e ook shelves. Bo ok shelf ? costs '1

per unit, re%uires si& s%uare feet of floor space, and holds eight cuic feet

of ooks . Book shelf @ cos ts '2 per unit , re%uires eight s%uare feet of

f loor space, and holds twelve cuic feet of ooks. The purchase udget is

'1$. The l irary has roo! for no !ore than 2 s%uare f ee t of ook

shelves. 5ow !any of each !odel should e ought, to !a&i!ize storage

vo lu !e* +?/, @ ")

linear programming sheet

Documents