W;WSuppose very gram of whea,*;rovidesq.l g of proteins and0.L5
g of catbohydrates,and he corresponding alues or rice areQ.05g
and0,1g respectiyely.WhqatcostsRs5 and rice Rs 79 per kilogram.
Therminimum daily requirementsof proteins andcarbohydratesor an
averageman?re'50 g and 200 g respectively. n what quantitiesshould
wheat and rice be mixed in the daily diet to provide the minimum
dailyrequirementsof proteins and carbohydratesat minimulq cost,
assuming hat bothwheat andrice are o be taken n the diet.A firm
manufactureswo typesof products,A and B, and sells hem at a profit
of Rs 5per unit of type A anclRs 3 per unit of type B. Each product
is processedon twomachines,Mr and Mz Oneunit of type A requiresone
minute of processing ime onM1 and fwo minutes of processing ime on
I\dz;whereasone unit of type B requiresone minute of processing
imr: on M1 andoneminute on M2. MachinesMr andM2
arerespectivelyavailable for at most 5 hours and 6 hours in a day.
Find out how manyunits of each ype of product should he frm
producea day n order to maximize theprofit. Solve heproblem
graphically.An aeroplane f an airline can carrya maximumof 200
passengers. prolftfof Rs.400is made on eachfirst-class ticket and a
profit of Rs.300 s madeon each economy-class icket. The airline
rservesat least 20 seats or first class. However, at least4times as
many passengersprefer to travel by economy class than by first
class.Determinehow many of each ype of tickets must be sold in
order to maximize theprofit for the airline. What is the
maximumprofit?A companymakes wo types r:f belts,A and B. Profits on
thesebelts beingRs.4 andRs.3 each respectively.Eachbelt of type A
requires wice asmuch time as a belt oftype B, and f all beltswere
of type B, the companycould make 1000beltsper day.The supply of
leather s sufficient for only 800beltsper day (bothA andB
combined).At the most 400 buckles for belt of type A and 700 for
thoseof type B are availableper day. How many belts of each ype
should the companymake per day so as tomaximize heprofit?A small
firm manufactures ecklaees nd bracelets.The total number of
necklaces ndbraceletshat t canhandleper day s at most24.It takes
hour to makea bracelet ndhalf anhour to make a necklace.The
maximumnumber of hours availableper day is16. f theprofit on a
necklace s Rs.100and hat on a bracelet s Rs.300,how many ofeach
shouldbe produceddailv to maximize the profit? It is being given
that at leastoneof eachmustbeproduceC..A man hasRs.1500o
purcbaseice andwheat.A bagof rice anda bag of
wheatcostRs.180andRs.120 espectively. e has a storage apacity f 10
bagsonly. He earnsaprofit of Rs.ll andRs.8pr;1bag of rice andwheat
respectively.How many bagsofeachmust he buy to make
rnaximumprofit?Two tailors,A and B, ea,:nRs.300andRs.400per day
respectively.A can stitch6shirts and4 pairs of troulrerswhile B can
stitch 10 shirts arrd4 pairs of trousersperday. How many days
sh.ouldeach of them work if it is desired o produceat least60shirts
and32pairsof trousersat a minimum laborcost?A dealerwishes to
purchasea number of fans and sewing machines.He has onlyRs.5760 o
invest and hasapaceor at most20 items.A fan costshim Rs.360and
asewingmachine,Rs.240.He expectso gain Rs.22 on a fan and Rs.18 on
a sewingmachine.Assuming hat he (,ansell all the itemshe can buy,
how shouldhe invest hemoney n order o maximize theprofit?
