1. two produc products ts are manufact manufactur ured ed sequenti sequentially ally on two machine. machine. the time is 8 hour hours s per per day day and and may may be incr increa ease sed d by up to 4 hour hours s of over overti time me,, if necessary, at an additional cost of 100 dollars per hour. the table below gives the production rate on the two machine as well wel l as the price per unit of the two products. determine the optimum production schedule and the recommended use of overtime, if any. dua produk yang diproduksi secara berurutan pada dua mesin. waktu adalah 8 jam per hari dan dapat ditingkatkan hingga 4 jam lembur, jika perlu, dengan biaya tambahan tambahan 100 dolar per jam. tabel di bawah ini memberikan memberikan tingkat tingkat produksi produksi pada dua mesin serta harga per unit dari dua produk. produk. menentukan menentukan jadwal produksi yang optimal dan penggunaan yang disarankan lembur, jika ada.
%achine 1 %achine $ rice per unit !'#
roduction rate !unit"hour# roduct 1 & 8 1 10
roduct $ & 4 11 8
2. Coalco Coalco produc produces es coal at three three mines and ships ships it to four costum costumers. ers. The The cost per ton ton of producing coal, the ash and sulfur content (per ton) of the coal, and the production capacity (in tons) for each ea ch mine are given in table 1. The number of tons of coal demanded by each customer are given in Table Table 2. The cost (in dollars) of shipping a ton of coal from a mine to each customer is given in Table 3. It is reuired that the total amount of coal shipped contain at most !" ash and at most #" sulfur. $ormulate an %& that minimi'es the cost of meeting customer demands. Colcau Colcau mempro memprodu dusi si batu batu baru baru dari dari tiga tiga pertamb pertambang angan an dan mengir mengirimi iminy nyaa epada epada onsumen. iaya produsi batu bara per ton, ash dan sulfur yang mengandung (per ton) batu bara, dan apasitas produsi (dalam ton) untu setiap pertambangan ditun*uan oleh Table able 1. Inform Informasi asi banya banyanya nya perminta permintaan an batu batu bara bara (dalam (dalam ton) ton) oleh oleh masing masing+ma +masing sing onsumen disa*ian pada Tabel 2. iaya (dalam dolar) pengiriman batu bara per ton dari pertambangan e setiap onsumen bisa dilihat pada Tabel Tabel 3. andungan masimal ash dan sulfur dalam batu bara setiap ali pengiriman berturut+turut adalah !" dan #". uatlah formul formulasi asi %& yang yang bertu* bertu*uan uan memini meminimal malan an biaya biaya untu untu bisa bisa memenu memenuhi hi permint permintaan aan onsumen.
%ine 1
roduction cost !'# &0
(able (able 1 )apaci *sh conten contentt !(ons# ons# ty 1 $0 0,08
+ulfur +ulfur conten contentt !( !(ons# ons# 0 ,0 &
$ -
&& $
100 140
0,0 0,04
0,04 0,0-
(able $ )ostumer 1 80
)ostumer $ 0
%ine 1 $ -
)ostumer 0
(able )ustomer $ 8 / 1$ -
1 4 / 8
)ustumer 4 40
4 1$ 11 &
-. )hemco produces - chemicals , ), and 2. (hey begin by purchasing chemical * for a cost of '"100 liters. 3or an additional cost of '- and the use of - hours of skilled labor, 100 liters of * can be transformed into 40 liters of ) and 0 liters of . )hemical ) can either be sold or processed further. t costs '1 and takes 1 hour of skilled labor to process 100 liters of ) into 0 liters of 2 and 40 liters of . 3or each chemical the sales price per 100 liters and the ma5imum amount !in 100s of liters# that can be sold are given in (able 1. * ma5imum of $00 labor hours are available. 3ormulate an 6 whose solution will tell )hemco how to ma5imi7e their prot.
(able 1 )hemicals rice !'# %a5 demand
1$ -0
) 1 0
2 $ 40
4. 2onovan enterprises produces electric mi5ers. 2uring the ne5t four quarters, the following demands for mi5ers must be met on time quarter 1 9 4000: quarter $ 9 $000: quarter - 9 -000 quarter 4 9 10000. ;ach of donovan
>umber of daily trip on route *ircraft (ype
)apacity !pasange rs#
>umber of aircraft
1
$
-
4
1 $ 2aily number of customer
&0 -0 $0
& 8 10
4 &
$ &
$ 4
1 $ $
1000
$000
/00
1$00
(he associated cost, including the penalties for losing customers because of space unavailability, are *ircraft type 1 $ enalty !'# per lost customer
1 1000 800 00
?perating cost !'# per trip on route $ 1100 1$00 /00 1000 800 800
40
2etermine the optimum allocation associated number of trips.
&0
4&
4 1&00 1000 /00 0
of aircraft to routes and determine the
. (hree types of coal, )1, )$, and )- are pulveri7ed and mi5ed together to produce &0 tons per hour needed to power a plant for generating electricity. (he burning of coal emits sulfur o5ide !in parts per million# wich must meet the ;vironmental rotection *gency !;*# specication of at most $000 parts per million. (he following table summari7es the data of the situation.
+ulfur !parts per million# ulveri7ed capacity !ton"hour# )ost per ton -etermine the optimal mi the coals. . adgadgadg
)1 $&00 -0 '-0
)$ 1&00 -0 '-&
)100 -0 '--
