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 gallant 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 produce 20 gallons of regular and 20 gallon, of deluxe .it costs $70 per hour lo operate Plant A. $98 per hour to operate Plant H. and $130 per hour to operate Plant M The company must produce at least 400 gallons of regular ice cream and at least 340 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. 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.) 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. The minimum production cost is $ (Round to the nearest cent as needed.) There is no minimum production cost.

Explanation / Answer

First, the knowns: 340 regular needed each day 400 gallons Plant A produces 20/10 Plant H proguces 10/20 Plant M produces 20/20 Now to find out how much each ice cream costs to produce each hour, then we can decide which plant to use the most: Plant P: 70/30= 2.33333333 Plant H:92/20=3.06666667 Plant M: 130/40=3.25 I set the whole thing up in MathCad so I could play with numbers and not have to do a million calculations. After doing all the calculations in matrix form: A:= Price x Quanity X hours H:=Price x Quanity X hours, etc... And then I would add up A+H etc... to find out quantity vrs. price... And Got this answer.... Plant A runs for: 14 hours. Plant B runs for 8 hours. Plant C runs for 2 Gives us the exact need of 400/340 at 2107.92 The cheapest is: Plant A runs for: 16 hours. Plant B runs for 9 hours. Plant C runs for 0 Gives us the exact need of 410/340 at 2101.91 All the calculations were done with no round off-- or very little, I think to the millionths place, untill the end, so the exact answer my vary due to round-off error. Hope this helps and Good Luck!

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