Question

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

Plant A produces 40 gallons of regular ice cream and 20 gallons of deluxe ice cream.


Plant H produces 20 gallons of regular ice cream and 40 gallons of deluxe ice cream,


and Plant M produces 40 gallons of regular and 40 gallons of deluxe.



It costs $60 per hour to operate Plant A, $92 per hour to operate Plant H, and $140 per hour to operate Plant M. The company must produce at least 350 gallons of regular ice cream and at least 240 gallons of deluxe ice cream each day.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.)

Answer 1

A = 8hrs

H = 3hrs

M = 0hrs

Explanation:

Let a be the working hours of plant A.

Let b be the working hours of plant H.

Let c be the working hours of plant M.

∴ Hours of plants A,H,M are a,b,c respectively.

We have to minimize the cost of production, Z = 60a + 92b + 140c

Regular ice cream: 40a + 20b + 40c = 350

Deluxe ice cream: 20a + 40b +40c =240

Where a>=0, b>=0, c>=0

So, by solving this, a= 7.67, b= 2.77,c= 0

So working hours of plant A = 8 hrs

Working hours of plant H = 3 hrs

Working hours of plant M = 0 hrs

Answer 2

Answer explained below

Explanation:

Let a be the working hours of plant A.

Let b be the working hours of plant H.

Let c be the working hours of plant M.

We have to minimize , Z = 60a + 92b + 140c

subject to constraint , 40a + 20b + 40c >=350

20a + 40b + 40c >=240

where a>=0 , b>=0 ,c>=0

So ,by solving this , a = 7.67 , b= 2.17 , c = 0

So ,working hours of plant A = 8 hrs

working hours of plant H = 3 hrs

working hours of plant M = 0 hrs