Grasshopper

algorithmic modeling for Rhino

rectangular membrane of minimal area

I've a problem making a membrane of minimal area which fulfills:
-AG : 4 Anchor ground points; AT : 1 Anchor top point
-Ground projection: rectangel a x b
-Min. hight inside the blue line: 2.50 m
-Area of blue line: min. 80% of the rectangel a x b
-Max. hight h of the top point: h,max = a
-Min. Volume between rectangel a x b and membrane: 500 m3
Can anyone help me?

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