Zevon Enterprises
Zevon Enterprises provides services for clients worldwide and to protect all parties to this course as well as Zevon, we shall refer to those services as X1, X2, and X3. Each of these services has its own special mix of needs for the resources the company has at its disposal. The X1 product requires three lawyers, seven guns, and $6,000; the X2 product requires two lawyers, five guns, and $4,000; and the X3 product requires four lawyers, six guns, and $7,000. Zevon has access to 5,000 lawyers, 10,000 guns, and $15,000,000. For ease of conversation, Zevon employees usually speak about dollars as "per thousand" so one of them asking for $7 means that they really need $7,000.
Zevon's demand is variable depending on what they charge for it. For example, the X1 product's demand is 200 - 2.25p1. The demand for X2 is 300 - 3p2, and the demand for X3 is 400 - 3.5p3. The per unit profit for X1 through X3 can be calculated by subtracting the per unit cost from the sales price, so for X1, the profit is p1 - 2.25, for X2 the profit is p2 - 3, and for X3 the profit is p3 - 3.5.
What is an appropriate objective function for this scenario?
• Max Z = (p1 - 2.25)X1 + (p2 - 3)X2 + (p3 - 3.5)X3
• Max Z = (p
1 - 2.25p
1) + (p
2 - 3)(300 - 3.00p
2) + (p
3 - 3.5)(400 - 3.50p
3)
• Max Z = 200X1 + 300X2 + 400X3
• Max Z = 2.25(p
1 - X
1) + 3(p
2 -X
2) + 3.5(p
3 - X
3)
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