Suppose the landlord really wants the back door to be installed. For too long he has had
to cut through the garage and he figures when he retires, this house will be a perfect
downsize home for him to move into. How should the constraint for the back door be
written if he uses the following scheme for decision variables?
A) x5 + x6 ≤ 1
B) x5 + x6 = 1
C) x5 - x6 ≤ 1
D) x5 - x6 = 1
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 forX1 through X3 can be calculated by subtracting
the per unit cost from the sales price, so for X1, the profit is p1 - 25, for X2 the profit is
p2- 3, and for X3 the profit is p3- 3.5.