OPRS

OPRS

#1Noda brewing co produces beer and ale. Beer sales for \$10 per barrel and ale sells \$5 per barrel. Producing a barrel of beer requires 6lbs of corn and 3 lbs of hops. Producing a barrel of ale requires 3 lb of corn and 2 lb of hops. Sixty pounds of corn and 25 lbs of hops are available. Formulate the LP.
TABLE
Beer|ALE
SELL| 10,5
CORN |6,3
HOPS|3,2

max z= 10x1+5x2
s.t 6x1+3x2≤60
3x1+2x2≤25
x1,x2≥0

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#2.

Labs manufactures mechanical heart valves from
the heart valves of pigs. Different heart operations require
valves of different sizes. U.S. Labs purchases pig valves
from three different suppliers. The cost and size mix of the
valves purchased from each supplier are given in Table 3.
Each month, U.S. Labs places one order with each supplier.
At least 500 large, 300 medium, and 300 small valves must
be purchased each month. Because of limited availability of
pig valves, at most 700 valves per month can be purchased
from each supplier. Formulate an LP that can be used to
minimize the cost of acquiring the needed valves.

SOLUTION: min z= 5x1+4x2+3x2
s.t .4x1+.3x2+.2x2≥500
4x1+.35x2+.2x3≥300
.2x1+.35x2+.6x3≥300
x1≤700
x2≤700
x3≤700
x1,x2,x3≥0
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#3
A post office requires different numbers of full-time employees on different days of the week. The number of full-time employees required on each day is given in the table. Union rules state that each full-time employee must work five consecutive days and then receive two days off. The post office wants to meet its daily requirements using only full-time employees. Formulate an LP that the post office can use to minimize the number of full-time employees that must be hired.

x1=ees start on mon
x2=ees start on tues
x3=ees start on wed
x4=ees start on thurs
x5=ees start on fri
x6=ees start on sat
x7=ees start on sunda

min z= x1+x2+x3+x4+x5+x6+x7
s.t
x1+x4+x5+x6+x7≥17
x2+x5+x6+x7+x1≥13
x3+x6+x7+x1+X2≥15
x4+x7+x1+x2+x3≥19...