For the following problem, just do everything necessary to set up the initial si

Question

For the following problem, just do everything necessary to set up the initial simplex tableau. Do not solve the problem A food processing company produces regular and deluxe ice cream at 3 plants. Per hour of operation, the plant in Raleigh produces 27 gallons of regular ice cream and 12 gallons of deluxe ice cream. The Greensboro plant produces 15 gallons of regular and 20 gallons of deluxe per hour, and the Cary plant produces 26 gallons of regular and 20 gallons of deluxe per hour. It costs $75 per hour to operate the Raleigh plant, $85 per hour to operate the Greensboro plant, and $80 per hour to operate the Cary plant. The company needs to produce at least 80 allo ,of regular ice cream and at least 270 gallons of deluxe ice cream for a special event. How many hours should each plant be operated to produce the required ice cream at the minimum possible cost? Use the following variable names: x-# hours to operate Raleigh plant y-# hours to operate Greensboro plant 2-# houre to operate Cary plant c -Cost (a) Give the constraint regarding the amount of regular ice cream that must be produced. (Write your constraint in a form like this: 29x + 37y + 50z >= 250.) Give the constraint regarding the amount of deluxe ice cream that must be produced Give the Cost function. (write your constraint in a form like this: C = 5x + 9y + 33z.) (b) Give the numerical value of the number in column one of the initial simplex tableau that can be used as the first pivot element. (For example, if it were the number -83 somewhere in column one, just type: -83) Give the numerical value of the number in column two of the initial simplex tableau that can be used as the first pivot element.

Explanation / Answer

a) 27x+ 15 y + 26 z>= 380   (regular icecream)

12x + 20y +20 z >= 270    (deluxe icecream)

cost function

C = 75*x + 85y + 80 Z

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