I am not sure how to visualize the following three equations

F1(P1)= 561 + 7.92 P1+ 0.00156 P1^2

F2(P2)= 310 + 7.85 P2 + 0.00194 P2^2

F3(P3) = 78 + 7.97 P3 + 0.00482P3^2

150 <= P1 <= 600

100 <= P2 <= 400

50 <= P3 <=200

P1+P2+P3 = 850

This is an optimisation problem with limits. Do I consider each of the functions on their own plane - for example F1(P1) would be on the xy plane. F2(P2) would be on the zx plane and F3(P3) would be on another plane. P1+P2+P3 would then be a plane that cuts each of them and we find the gradient vector from there.

F1(P1)= 561 + 7.92 P1+ 0.00156 P1^2

F2(P2)= 310 + 7.85 P2 + 0.00194 P2^2

F3(P3) = 78 + 7.97 P3 + 0.00482P3^2

150 <= P1 <= 600

100 <= P2 <= 400

50 <= P3 <=200

P1+P2+P3 = 850

This is an optimisation problem with limits. Do I consider each of the functions on their own plane - for example F1(P1) would be on the xy plane. F2(P2) would be on the zx plane and F3(P3) would be on another plane. P1+P2+P3 would then be a plane that cuts each of them and we find the gradient vector from there.

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