Question: The linear programming problem whose output follows is used to determine how many bottles of fire red nail polish (x ₁ ), bright red nail polish (x ₂ ), basil green nail polish(x ₃ ), and basic pink nail polish(x ₄ ) a beauty salon should stock. The objective function measures profit; it is assumed that every piece stocked will be sold. Constraint 1 measures display space in units, constraint 2 measures time to set up the display in minutes. Note that green nail polish does not require any time to prepare its display. Constraints 3 and 4 are marketing restrictions. Constraint 3 indicates that the maximum demand for fire red and green polish is 25 bottles, while constraint 4 specifies that the minimum demand for bright red, green and pink nail polish bottles combined is at least 50 bottles.

MAX 100x ₁ + 120x ₂ + 150x ₃ + 125x ₄

Subject to i. x ₁ + 2x ₂ + 2x ₃ + 2x ₄ \(\le \) 108

ii. 3x ₁ + 5x ₂ + x _{4 \(\le \)} 120

iii. x ₁ + x ₃ \(\le \) 25

iv. x ₂ + x ₃ + x _{4 \(\ge \)} 50

x ₁ , x ₂ , x ₃ , x _{4 \(\ge \)} 0

Optimal

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Solution: The downloadable solution consists of 3 pages
Deliverable: Word Document