Maximize nonlinear function with linear constraints

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I would like to have Sage maximize 60 * 5^{x0} *4^{x1} * 3^{x2}, where x0, x1, x2 are nonnegative integers such that

x0+x1+x2=2k-3 and x1+2*x2 >= 3k-3,

where k is any nonnegative integer such that 3<= k <=20. I would like to create a loop so that Sage does this for me for each of these values of k.

I know that Sage has a tool called minimize_constrained, but I can't find a tool called "maximize_constrained". Please help! Thank you in advance :-)