Table 3.9: Zen Nail Spa Zen Nail Spa in Albuquerque stocks four colors of nail polish, pink (Pi), ...

Table 3.9: Zen Nail Spa
Zen Nail Spa in Albuquerque stocks four colors of nail polish, pink (Pi), white (W), blue (B), and purple (Pu). Depending on the color requested, the client pays a different price due to drying times and need to touch up coverage. The pink color yields a profit of $100, white $150, blue $120, and purple $125. Bottles of pink nail polish take up one unit of shelf space and all other colors take up two units each. The total shelf space available in the storage cabinet and display is 108 units. Three of the colors (all except blue) require some mixing time. Pink takes three minutes, white takes five minutes, and purple takes a minute. The mixing technician can devote only two hours to these duties as she also runs the register at the Spa and the laser tag next door. Past demand has demonstrated that demand for pink and blue do not exceed 25 units each per week. However, the minimum weekly demand for white, blue and purple colors must be at least 50 units.

The sensitivity report appears below:

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Max Z = 4x1 + 3x2
Subject to: 6x1 + 2x2 ≤ 24
15x1 + 20x2 ≤ 60
x1, x2 ≥ 0
Determine the sensitivity range for each constraint.