Assume that a monopolist produces two software programs, one to solve math problems $($M$)$ and the other to solve statistics problems $($S$).$ There are only three consumers $($A$,$ B$,$ and C$)$ who are interested in them. Their preferences are as follows:

i$.$ Consumer A values M at $$50$ and S at $$30.$

ii$.$ Consumer B values $M$ at $$80$ and $S$ at $$40.$

iii. Consumer C values M at $$100$ and S at $$50.$

A$.$ Are demand values among consumers negatively or positively correlated?

B$.$ If the firm's average and marginal cost is $0,$ will it pay to sell $M$ and $S$ separately or as a pure bundle?

C$.$ How would your answer to part $B$ change if consumer demand values were negatively correlated?