Hilo Nail Spa Hilo 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.

1) How much shelf space will be left unused? How many minutes of idle time remain for mixing?

2) Use the LP output to answer these two questions.

(a) To what value can the per bottle profit on blue nail polish drop before the solution would change?

(b) By how much can the per bottle profit on purple nail polish increase before the solution would change?

3) Use the LP output to answer these two questions.

(a) how much are you willing to pay for an additional unit of shelf space? By how much?

(b) What is the impact on profit if white, blue and purple stocking levels must equal at least 53 units (from 50 to 53)?

4) You are offered the chance to obtain more shelf space. The offer is for 10 units and the total price is $700. What should you do? Why?

The sensitivity report appears below