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Jack is deciding how to spend the $6 budget he has allocated for today's telephone calls. There are only two people he intends to call: his girlfriend Jill, and his old high school friend, Steve. Jack's love for Jill is such that he could talk to her forever; the marginal utility of a minute talking to Jill is a constant ten utils, regardless of the number of minutes he talks. Steve usually has a lot of interesting news, but he becomes dull and boring after awhile; the marginal utility of talking to Steve is given by the equation:
MU = 60 - 2M
where M is the number of minutes they have talked so far. So, the first minute gives Jack 58 utils, the second minute gives him 56 utils, etc.
It costs 5 cents per minute to call Jill, and 10 cents per minute to call Steve, who lives farther away.
How should Jack allocate his budget of $6 to maximize his total utility? In other words, how many minutes should Jack spend talking to Steve today, and how many minutes talking to Jill?
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