What would be the LP model and constraints for this question? I have figured out

Question

What would be the LP model and constraints for this question?

I have figured out it would start with

Let P the amount of resource;

ri be the amount of resource required on the ith day where r1 = #unit required on monday, ..., r7= ~ sunday, ri+7=ri, i=1,...,7;

xi be the amount of resource used on the ith day where x1 = #unit consumed on monday, ..., x7= ~ sunday, xi+7=xi, i=1,...,7?;

min z = P

subject to

r1=17 ..., r7=11

P >= xi + xi+1 + ,..., + xi+4, i=1,...,7

ri= xi + [P - xi + xi+1 + ,..., + xi+4], i=1,...,7 (the square bracket means the amount to be renewed)

All variables are non-negative

Please review my solution and let me know where to fix.

Explanation / Answer

Let P the amount of resource;

ri be the amount of resource required on the ith day where r1 = #unit required on monday, ..., r7= ~ sunday, ri+7=ri, i=1,...,7;

xi be the amount of resource used on the ith day where x1 = #unit consumed on monday, ..., x7= ~ sunday, xi+7=xi, i=1,...,7;

min z = P

subject to

r1=17 ..., r7=11

P <= xi + xi+1 + ,..., + xi+4, i=1,...,7

ri= xi + [P - xi + xi+1 + ,..., + xi+4], i=1,...,7 (the square bracket means the amount to be renewed)

All variables are non-negative

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