A company produces regular and deluxe ice cream at three plants. Per hour of ope

Question

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 $60 per hour to operate Plant A, $72 per hour to operate Plant H, and $130 per hour to operate Plant M. The company must produce at least 420 gallons of regular ice cream and at least 330 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 day, and Plant M should operate for hours per day. Round to the nearest tenth as needed.) hours per day, Plant H should operate for hours per O B. There is no optimal solution.

Explanation / Answer

let plant A operate for x hours , plant H for y hours . plant M for z hours

setting up the constraint

20 x + 10y + + 20 z >= 420

10x + 20 y + 20 z >= 330

since there are 3 unknown variables and only two inequalities

we cannot solve this system

hence , no optimal solution

objective functon is

P = 60x + 72 y + 130 z

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