Linda loves buying shoes and going out to dance. Her utility function for pairs of shoes, S$,$ and the number of times she goes dancing per month, T$,$ is U$($S$,$ T$)=2$ST$,$ so MUS $=2$T and MUT $=2$S$.$ It costs Linda $$50$ to buy a new pair of shoes or to spend an evening out dancing. Assume that she has $$500$ to spend on shoes and dancing.