i developing equilibrium model producers weight benefits , costs choose optimal time work. however, relevant benefit , cost functions both rational, results in complex first-order derivative of problem. when parameter values introduced, systems of 3 equations in 3 variables following:
eq1 = (10940*((12034*x)/35 + (1094*y)/5 + (2734*z)/25))/(7*(((12034*x)/35 + (1094*y)/5 + (2734*z)/25)^2 + 640000)) - (10940*((12034*x)/35 + (1094*y)/5 + (2734*z)/25)^3)/(7*(((12034*x)/35 + (1094*y)/5 + (2734*z)/25)^2 + 640000)^2) == x^3/5184
eq2 = (10940*((1094*x)/15 + (51418*y)/105 + (2734*z)/25))/(7*(((1094*x)/15 + (51418*y)/105 + (2734*z)/25)^2 + 640000)) - (10940*((1094*x)/15 + (51418*y)/105 + (2734*z)/25)^3)/(7*(((1094*x)/15 + (51418*y)/105 + (2734*z)/25)^2 + 640000)^2) == y^2/576
eq3 = (5468*((1094*x)/15 + (1094*y)/5 + (30074*z)/75))/(5*(((1094*x)/15 + (1094*y)/5 + (30074*z)/75)^2 + 490000)) - (5468*((1094*x)/15 + (1094*y)/5 + (30074*z)/75)^3)/(5*(((1094*x)/15 + (1094*y)/5 + (30074*z)/75)^2 + 490000)^2) == z^2/576
it has taken around 48 hs matlab find solutions such systems of equations - when find them - using solve command. there more efficient way complete task? (i have pretty clear guess @ solutions should like: 3 outcome variables expected within [0,12] interval.)
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