A New Pizza Restaurant Is Moving into Town $$x _ { j } = \left\{ \begin{array} { l } 1 , \text { if location } j \text { is selected } \\0 , \text { otherwise }\end{array} \right.$$

question 47

Multiple Choice

A new pizza restaurant is moving into town. The owner is considering a number of potential sites and would like to minimize the initial investment involved with purchasing locations. However, the owner is very concerned about delivery time and wants to make sure that every neighborhood in the city can have a pizza delivered in 15 minutes or less. The owner has divided the city into 10 neighborhoods (A-J) and is currently considering a total of 8 different locations. To help with the decision, the owner formulated the following linear programming model:
Min 100x1 + 120x2 + 90x3 + 135x4 +75x5 + 85x6 + 110x7 + 135x8
s.t. x1 + x2 + x5 + x7 ? 1 {Neighborhood A constraint}
X1 + x2 + x3 ? 1 {Neighborhood B constraint}
X5 + x6 + x8 ? 1 {Neighborhood C constraint}
X1 + x4 + x7 ? 1 {Neighborhood D constraint}
X2 + x3 + x7 ? 1 {Neighborhood E constraint}
X3 + x4 + x8 ? 1 {Neighborhood F constraint}
X2 + x5 + x7 ? 1 {Neighborhood G constraint}
X1 + x4 + x6 ? 1 {Neighborhood H constraint}
X1 + x6 + x8 ? 1 {Neighborhood I constraint}
X1 + x2 + x7 ? 1 {Neighborhood J constraint} $$x _ { j } = \left\{ \begin{array} { l } 1 , \text { if location } j \text { is selected } \\0 , \text { otherwise }\end{array} \right.$$
Which of the locations is the most expensive?

• A) Location 1.
• B) Location 2.
• C) Location 3.
• D) Location 4.
• E) Location 5.

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Definitions:

Face Value

The nominal or dollar value printed on a financial instrument, such as a bond or stock certificate.

Premium

The amount paid for an insurance policy or the amount by which a bond or stock sells above its par value.

Straight-Line Amortization

A method of calculating equal amortization payments over an asset's useful life or a loan's term.

Interest Expense

The cost incurred by an entity for borrowed funds; this expense is reported on the income statement during the period in which the borrowing occurs.