Answer to Question #231108 in Operations Research for Ziya

Question #231108

2. A manufacturer produces two models of a certain product: model A and model B. There is a R20 profit on model A and an R35 profit on model B. Three machines M1,M2 and M3 are used jointly to manufacture these models. The number of hours that each machine operates to produce 1 unit of each model is given in the table: Model A Model B Machine M1 1 1 2 1 Machine M2 3 4 1 1 2 Machine M3 1 1 3 1 1 3 No machine is in operation more than 12 hours per day. Now let x be the number of model A made per day and y be the be the number of model B made per day. Then x and y satisfies the following constrains


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Expert's answer
2021-09-01T07:25:01-0400

"\\def\\arraystretch{1.5}\n \\begin{array}{c:c:c}\n & Model\\ A & Model\\ B \\\\ \\hline\n Machine\\ 1 & 3\/2 & 1 \\\\\n \\hdashline\n Machine\\ 2 & 3\/4 & 3\/2 \\\\\n \\hdashline\n Machine\\ 3 & 4\/3 & 4\/3 \\\\\n \n\\end{array}"

Let "x" be the number of model A made per day: "x\\geq0."

Let "y" be the be the number of model B made per day: "y\\geq0."

Machine 1 is in operation more than 12 hours per day:


"\\dfrac{3}{2}x+y\\leq12"

Machine 2 is in operation more than 12 hours per day:


"\\dfrac{3}{4}x+\\dfrac{3}{2}y\\leq12"

Machine 3 is in operation more than 12 hours per day:


"\\dfrac{4}{3}x+\\dfrac{4}{3}y\\leq12"


The answer is:


"x\\geq0, y\\geq0,\\dfrac{3}{2}x+y\\leq12,"


"\\dfrac{3}{4}x+\\dfrac{3}{2}y\\leq12, \\dfrac{4}{3}x+\\dfrac{4}{3}y\\leq12"


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