Suppose we wish to create a closed box with volume 1 m3m3, as cheaply as possibl

Question

Suppose we wish to create a closed box with volume 1 m3m3, as cheaply as possible. The material for the bottom and sides costs $10/m210/m2 and the material for the top costs $20/m220/m2. Which of the following is the correct cost function to be minimized (before using the constraint to eliminate a variable)?

Constrained Optimization Suppose we wish to create a closed bax with volume 1m3, as cheaply as possible. The material for the bottom and sides costs $10/m2 and the material for the top costs $20/m2. Which of the following is the correct cost function to be minimized (before using the constraint to eliminate a variable)? B 20a2+40ay O 30x2 4 O302+S0y O F None of the above

Explanation / Answer

i think you mean box with square base

let the length of box =x , width of box =x , height of box =y

area of bottom =x2,area of top =x2,area of each of four sides =xy

cost of bottom =10x2,area of top =20x2,area of each of four sides =10xy

total cost =10x2+20x2+(4*10xy)

total cost =30x2+40xy

cost function is  30x2+40xy

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