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polyfrag

Applying calculus

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I'm determining the price of resources based on the cost of inputs plus a profit of $0.01. There's two-way dependencies / positive feedback that require calculus. The price should approach a fixed value because each time the input increment is smaller and smaller.

Now how do I put this into an integral equation so I can solve it?

X = price of electricity
Y = price of chemicals
1 transport = average 3.9375 fuel
Z = price of fuel

refinery: Z = ( $0.09886947584789311408016443987668/crude*3 crude + X*1 electricity + Y*1 chemicals + Z*3.9375*1 transport ) / 21 fuel + $0.01

reactor: X = ( $0.03440657759506680369989722507708/uronium*1 uronium + 10 labour*$0.01/labour + Z*3.9375*1 transport ) / 10 electricity + $0.01

chem plant: Y = ( $0.01/labour*10 labour + X*10 electricity ) / 42 chemicals + $0.01

Edited by polyfrag

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Never mind, don't need calculus

 

Solving for Z

 

Z = ( $0.09886947584789311408016443987668/crude*3 crude + (( $0.03440657759506680369989722507708/uronium*1 uronium + 10 labour*$0.01/labour + Z*3.9375*1 transport ) / 10 + $0.01) + (( $0.01/labour*10 labour + ( ( $0.03440657759506680369989722507708/uronium*1 uronium + 10 labour*$0.01/labour + Z*3.9375*1 transport ) / 10 electricity + $0.01)*10 electricity ) / 42 + $0.01) + Z*3.9375*1 transport ) / 21 fuel + $0.01

 

= ( $0.29660842754367934224049331963004 + (( $0.03440657759506680369989722507708 + $0.1 + Z*3.9375) / 10 + $0.01) + (( $0.1 + (( $0.03440657759506680369989722507708 +$0.1 + Z*3.9375) / 10 + $0.01)*10 ) / 42 + $0.01) + Z*3.9375 ) / 21 fuel + $0.01

 

= ( $0.29660842754367934224049331963004 + $0.023440657759506680369989722507708 + Z*3.9375/10 + $0.43440657759506680369989722507708 / 42+ Z*3.937510 / 42 + $0.01 + Z*3.9375 ) / 21 fuel + $0.01

 

= ($0.33004908530318602261048304213774 + Z*(3.9375/10+3.937510/42+3.9375) + $0.43440657759506680369989722507708 / 42) / 21 fuel + $0.01

 

= ($0.34039209905544951793667107130624 + Z*(0.39375+0.09375023809523809523809523809524+3.9375) / 21 fuel + $0.01

 

= $0.02620914757406902466365100339554 / fuel + Z*0.21071429705215419501133786848073

 

Z (1-0.21071429705215419501133786848073) = $0.02620914757406902466365100339554 / fuel

 

Z = $0.02620914757406902466365100339554 / 0.78928570294784580498866213151927 / fuel

 

= $0.03320616029934709868104743489958 / fuel

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