Chapter 6.2, Problem 47E

Resource Allocation One day, Gillian the magician summoned the wisest of her women. “Devoted sisters of the Coven,” she began, “I have a quandary: As you well know, I possess great expertise in sleep spells and shock spells, but unfortunately, these can be a drain on my aural energy resources, and I would like my net expenditure of aural energy to be a minimum yet still meet my commitments in protecting the Sisterhood from the ever-present threat of trolls. Specifically, I have estimated that each sleep spell keeps us safe for an average of 3 hours, while every shock spell protects us for only 1 hour. We certainly require enough protection to last 24 hours of each day and possibly more, just to be safe. At the same time, I have noticed that each of my sleep spells can immobilize two trolls at once, whereas one of my powerful shock spells can immobilize four trolls at once. We are faced, my sisters, with an onslaught of as many as 26 trolls per day! Finally, as you are no doubt aware, the Bylaws of the Coven dictate that for a magician to remain in good standing, she should cast no more shock spells than sleep spells, whereas-and I quote from Bylaw 33c-“The number of sleep spells shall never exceed thrice that of shock spells by more than three.” What do I do, oh Wise Ones?” How would they respond if:

a. Each sleep spell uses 50 therms of aural energy and each shock spell uses 20 therms?

b. Each sleep spell uses 40 therms of aural energy whereas each shock spell boosts aural energy by 10 therms?

c. Each sleep spell uses 10 therms of aural energy whereas each shock spell boosts aural energy by 40 therms?

[HINT: See Example 4.]