A university plans to use instructors and graduate assistants in aresearch proje

Question

A university plans to use instructors and graduate assistants in aresearch project. The university needs at least 400 hours of laborspent in gathering data, with each instructor spending 8 hours andeach graduate student spending 20 hours gathering data. After thedata are gathered, at least 304 hours are required for processing.Each instructor can process data for 8 hours and each graduateassistant for 4 hours. If instructors cost $10 per hour andgraduate assistants cost $7 per hour, find the number of each theuniversity should use for minimum cost. Assume that the universityuses the same instructors and graduate assistants to gather andprocess the data.

Explanation / Answer

let there be x instructors and y assistants 8x+20y=400...(1) again in processing 8x+4y=304....(2) subtracting (2) from (1) 16y=96 y=6 putting y=6 in (1) 8x+120=400 8x=280 x=35

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