A semiconductor manufacturer has three different types of silicon wafers in stock to manufacture its three varieties of computer chips. Some wafer types cannot be used for some chips, but there are two alternatives for each chip. The table that follows shows the cost and on-hand supply of each wafer type, the number of each chip needed, and a score (0 to 10) of the appropriateness match of each wafer type for making each chip.

The company would like to minimize the total cost of the wafers used while maximizing the total match score.

(a) Briefly explain how this problem can be modeled by the multiobjective LP min 15x1,1 + 15x1,2 + 25x2,1 + 25x2,3 + 30x3,2 + 30x3,3 max 7x1,1 + 8x1,2 + 10x2,1 + 6x2,3 + 10x3,2 + 10x3,3 s.t. x1,1 + x1,2 … 500 x2,1 + x2,3 … 630 x3,2 + x3,3 … 710 x1,1 + x2,1 = 440 x1,2 + x3,2 = 520 x2,3 + x3,3 = 380 all xi, j Ú 0

(b) and

(c) as in Exercise 8-1.

Transcribed Image Text:

Wafer Unit On Type Chip Match Cost Hand 1 2 3 1 7 8 15 500 2 10 6 25 630 3 10 10 30 710 Need 440 520 380