1. A firm manufactureswo types of products,A andB, andsells hem
at aprofit of Rs.2on type A and Rs.2 on type B. Eachproduct is
processedon two machines,Ml andM2. Type A requiresone minute of
processing ime on Ml and two minuteson M2.Type B requires one
minute on Ml and one minute on M2. The machine Ml isavailable or
not more than 6 hours 40 minuteswhile M2 is available or at most
10hours a day.Find how many productsof each ype the firm
shouldproduceeachdayin order o getmaximumprofit.2. A
manufacturerproduces wo types of soapbarsusing two machines,A and
B. A isoperatedor 2 minutesand B for 3 minutes o manufacturehe
first type,while it takes3 minuteson machineA and 5 minuteson
maehineB to manufacturehe secondype.Each machinecan be operatedat
the most for 8 hoursper day. The two fypesof soapbarsare sold at a
profit of Rs.0.25and Rs.0.50each.Assumingthat the manufacturercan
sell all the soapbars he can manufacture,how many bars of soap of
each ypeshouldbe manufactured er rJay o as o maximizehis profit?3.
A toy companymanufactureswo types of dolls, A and B. Each doll of
type B takestwice as ong to produceas one of typeA, and he
companywould have ime to makea maximum of 2000 per day, if it
producesonly type A. The supply of plastic issufficient to produce
1500dolls per day (both A and B combined).Type B requiresafancy
dress of which there are only 600 per day available. If the
companymakesprofits of Rs.3 and Rs.5 per doll respectivelyon dolls
A and B, how many of eachshouldbe producedper day in order to
maximize theprofit? Also, find the maximumprofit.4. A small
manufacturerhasemployed5 skilled men and 10semiskilledmenand
makesan article in two qualities, a deluxe model and an ordinary
model. The making of adeluxe model requires 2 hours' work by a
skilled man and 2 hours work by asemiskilledman.The ordinarymodel
requires hour by a skilled manand3 hours bysemiskilledman. By union
rules, no man can work more than 8 hours per day.
ThemanufacturergainsRs.15on the deluxemodelandRs.10on the
ordinarymodel. Howmany of each ype shouldbe made n order to
maximize his total daily profit? Also,find the maximumdaily
profit.5. A diet for a sick person must contain at least 4000 units
of vitamins, 50 units ofmineralsand 1400calories.Two foods A and B
are availableat a cost of Rs.4 andRs.3per unit respectively. f one
unit of A contains200 units of vitamins, I unit ofminerals and40
calories,and I unit of B contains 100 units of vitamins, 2 units
ofminerals and 40 calories, ind what combinationof foods shouldbe
used o have heleastcost.6. A housewifewishes o mix together wo
kinds of food, X and Y in sucha way that themixture containsat
least l0 units of vitamin A, 12 units of vitamin B and 8 units
ofvitamin C.
If I kg of foodX costsRs.6and I kg of foodY costsRs.10, ind the
minimumcostofthe mixturewhich will produee he diet.
