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 $50 per hour to operate Plant A, $82 per hour to operate Plant H, and $120 per hour to operate Plant M. The company must produce at least 180 gallons of regular ice cream and at least 310 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. A. To minimize the cost of production, Plant A should operate forhours per day, Plant H should operate forhours per day, and Plant M should operate forhours per day. (Round to the nearest tenth as needed.) B. Is there an optimal solution? Part 2 What is the minimum production cost? Select the correct choice below and fill in any answer boxes within your choice. A. The minimum production cost is $ (Round to the nearest cent as needed.) B. Is there a minimum production cost?

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter5: Linear Inequalities

Section5.6: Graphing Ineualities In Two Variables

Problem 29PPS

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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 $50 per hour to operate Plant A, $82 per hour to operate Plant H, and $120 per hour to operate Plant M. The company must produce at least 180 gallons of regular ice cream and at least 310 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.

A. 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.)

B. Is there an optimal solution?