Hello, I was wondering if you d be able to help me with some linear program prob

Question

Hello,

I was wondering if you d be able to help me with some linear program problems? I am a graduate student and I am struggeling with my graded homework for the operatios research class. Can you pls help. It is so important, I am really strugeling in this class.

This is the following problem:

(1) A firm wants to determine its production rate over the next 6 months. Expected demand for its product is 30, 80, 90, 75, 80 and 100 units for months 1 through 6, respectively. The product is perishable and thus cannot be stored from month to month. The loss per unit not sold is $8, and the loss per unit short is estimated to be $15. Because of the nature of the production process, outputmust be maintained at some linear function over the time period. That is, if we begin with a production rate of 50, and end with 100 units in month 6, the intermediate production must lie on the straight line between 50 and 100. Formulate this problem and determine its model to be developed if we wish to minimize the total costs. [20 pts]

2) For question (1) above, If the production curve is a non- linear curve (y=mx 2 + b) , how would you determine the parameters to minimize the total cost ? [10 pts]

Thanks so much.

Any information would be helpful for me thanks.

Explanation / Answer

let xi = product i 30,80,90,75,100

contraints minimum

x1>=30

x2>=80

x3>=90

x4>=75

x5>=80

x6>=100

   50 >= x1 and x1>= 100

30x1+50x2+x3+x4 >=8

50x1+80x2+90x3>=15

x>=0.8

xb>=0.15

all variables >=0

minimize

x1+x2+x3+x4+x5+x6

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