Question

Question Help A company produces regular and deluxe ice cream at three plants. Per hour of operation, Plant A produces 20 gallons of regular ice cream and 10 gallons of deluxe ice cream. Plant H produces 10 gallons of regular ice cream and 20 gallons of deluxe ice cream, and Plant M produces 20 gallons of regular and 20 gallons of deluxe. It costs $70 per hour to operate Plant A, $78 per hour to operate Plant H, and $110 per hour to operate Plaht M. The company must produce at least 440 gallons of regular ice cream and at least 380 gallons of deluxe ice cream each day. How many hours per day should each plant operate in order to produce the required amounts of ice cream and minimize the cost of production? Select the correct choice below and fill in any answer boxes within your choice OA. To minimize the cost of production, Plant A should operate for hours per day, Plant H should operate for hours per day, and Plant M should operate for hours per day Round to the nearest tenth as needed.) O B. There is no optimal solution. What is the minimum production cost? Select the correct choice below and fill in any answer boxes within your choice O A. The minimum production cost is s (Round to the nearest cent as needed.) O B. There is no minimum production cost

Answer 1

Let Plant A operates x,haar, H opentes and plant mpsours. hun haurs Total cost , ズ=TA+18x2+"0x3 20 х ical Vavablkd 2

Iteration-1 70 78 110 MinRatio 440 20 10 M 440 1 0 0 20 20 380 10 20 (20) M 380 0 01 20 Z. Z- 820M 30M 30M 40M MI-MIM M C 30M-7030M-78 40M-110t-M-M 0 0 Positive maximum Z.-C is 40M-110 and its column index is 3. So, the entering variable is x3 Minimum ratio is 19 and its row index is 2. So, the leaving basis variable is A . The pivot element is 20. Iteration-2 70 78 110 0 MinRatio -10 (10) 10 19 38 110 19 20 Z = 60M+ 2090 10M 55 -10M 110 110-MM- Z-C M-15 1 10M+320M M. - Positive maximum Z, - C, is 10M- 15 and its column index is 1. So, the entering variable is x Minimum ratio is 6 and its row index is 1. So, the leaving basis variable is A . The pivot element is 10.

Iteration-3 110 70 78 MinRatio 10 10 16 32 10.6667 - 16 110 20 10 Z. Z- 2180 70 95 110- Z: - C Positive maximum Z, - C, is 17 and its column index is 2. So, the entering variable is x. Minimum ratio is 10.6667 and its row index is 2. So, the leaving basis variable is x3 The pivot element is Iteration-4 110 70 78 MinRati 50 15 30 32 15 296 31 15 15 34 31 43 15 15 Since all Z, -so Hence, optimal solution is arrived with value of variables as 32 5996 To minimize the cost of production, Plant A should operate for 50/3 hours per day, Plant H should operate for 32/3 hours per day, and Plant M should operates for 0 hours per day