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Question
A dealer wishes to purchase table fan and ceiling fans.He has Rs57,6000  to invest,and has space to store 40 items.A table fan cost Rs760 and ceiling fan cost Rs900.He can make profits Rs70 and Rs90 by selling a table fan and ceiling fan respectively.Assuming that he can sell all the fans that he can buy,formulate this problem as LPP,to maximize the profit.

Here's how I would set up this problem as  an LPP (Linear Programming Problem). The solution consists of determining the number of units (table or ceiling fans) the dealer should buy/sell. The function to maximize is the profit and the constraints are the number of units his facility holds as well as the amount of money he has to invest. So

Number of units: Nt = tables fans, Nc =ceiling fans; solve for Nt and Nc with Nt + Nc ≤ 40.

Cost of units: Ct = table fan, Cc = ceiling fan; constraint Ct + Cc ≤ 57,6000 = I

Profit per unit: Pt = table fan, Pc = ceiling fan; maximize Ptot = Pt + Pc.

MS Excel has an tool called Solver that solves these sorts of LPP problems and is fairly easy to implement (has tutorial).

This problem, as you state it, has some ambiguities. First of all, the Rs57,6000 (which I assume really means Rs 576,000 in more conventional notation) would enable the dealer to purchase far more than the 40 units, of either or both types, he could store. Also, the higher profit for the ceiling fan indicates that he should buy and sell only that type of fan. To wit, if the dealer only buys/sells one type of fan then

total profit for table fan: (I/Ct)(Pt) = (570,000/760)(70) = Rs53,053
(I/Cc)(Pc) = Rs57,000.

So something is fishy here (or I've made a mistake). Anyway, look over your problem and let me know if you have a follow-up

Randy

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#### randy patton

##### Expertise

college mathematics, applied math, advanced calculus, complex analysis, linear and abstract algebra, probability theory, signal processing, undergraduate physics, physical oceanography

##### Experience

26 years as a professional scientist conducting academic quality research on mostly classified projects involving math/physics modeling and simulation, data analysis and signal processing, instrument development; often ocean related

Publications
J. Physical Oceanography, 1984 "A Numerical Model for Low-Frequency Equatorial Dynamics", with M. Cane

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M.S. MIT Physical Oceanography, B.S. UC Berkeley Applied Math

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Also an Expert in Oceanography