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The question takes place over 3 time periods (0,1,2). Calculating for a discount rate of 10%, what s the optimal distribution for 1200 goods. Price of the goods are $50. Cost is (Xt^2)/20. B=1+10%=1.1

The equation that I am using is:

V0=pX0-c(X0) + B(pX1-cX1) + B^2(pX2-cX2) s.t. x0+x1+x2=1200

this becomes

p-c'(x0)=B(p-c'x1)-B^2(p-c'x2)

50-x0/10=55-1.1(x1)/10 - 60.5 - 1.2(x2)/10

555=x0-1.1(x1)+1.21(x2)

After that, I've tried everything that I can think of. The answers are supposed to be x0=409.4, x1=400.3, x2=390.3

Please help!!

Thanks everyone