Kiano, a telecommunications equipment manufacturer, manufactures PDAs (P), wireless handsets (H), and blackberrys (B). They have a limited supply of common parts---ethernet card (450 in inventory), antenna (250 in inventory), chipset (800 in inventory), battery/power supply (450 in inventory), LCD screen (600 in inventory)---that these products use. A PDA requites an ethernet card, 2 chipsets, a power supply, and 2 LCD screens. A wireless handset requires an ethernet card, an antenna, 2 chipsets, a power supply, and a LCD screen. A blackberry requires a chipset and a LCD screen. The profit on PDAs is $80, the profit on wireless handsets is $60, and the profit on blackberrys is $35. The following is a linear programming formulation of the problem.
Let
P = Number of PDAs produced
H = Number of wireless handsets produced
B = Number of blackberrys produced
We may write model for this problem as follows.
Maximize 80P + 60H + 35B
subject to:
(ethernet card constraint) P + H ? 450
(antenna constraint constraint) H ? 250
(chipset constraint) 2P + 2H + B ? 800
(power supply constraint) P + H ? 450
(LCD screen constraint) 2P + H + B ? 600
(non-negativity) P, H, B ? 0.
Implement the above model in Solver and make sure to choose Simplex as the solving method and to choose the option "Make Unconstrained Variables non-negative"---do not explicitly put in the non-negativity constraints in the model and using the sensitivity report only
answer the questions below:
a. Does the solution change if only 425 ethernet cards are available?
b. Is it profitable to produce Blackberrys? If not, by how much should the profit margin on Blackberrys be increased to make it profitable to produce Blackberrys?
c. Because of a change in production technology the profit margin on handsets has increased to $70. Should the production plan of Kiano change? What is their new profit?
d. 50 chipsets were found to be defective, making the number of available chipsets 750. What will the profit be in this situation?
e. Another supplier is willing to sell LCD screens to Kiano. However their prices for a LCD screen are $20 higher than what Kiano pays it's regular supplier. Should Kiano go ahead and purchase these electronic units? If yes, at most how many units should they purchase.
f. Kiano is considering introducing a new product (called the Revolutionary Communicator) that combines the wireless handset and PDA. This product uses an ethernet card, an antenna, 2 chipsets, 1 power supply, and 2 LCD screens, and is expected to make a profit of $100. Should Kiano produce the Revolutionary Communicator? Why or Why not?