Design a rectangular milk carton box of width w , length l , and height h which

Question

Design a rectangular milk carton box of width w, length l, and height h which holds 540 cm3 of milk. The sides of the box cost 5 cents/cm2 and the top and bottom cost 10 cents/cm2. Find the dimensions of the box that minimize the total cost of materials used. Give exact answers.

w = cm
l = cm
h = cm

Design a rectangular milk carton box of width w, length l, and height h which holds 540 cm3 of milk. The sides of the box cost 5 cents/cm2 and the top and bottom cost 10 cents/cm2. Find the dimensions of the box that minimize the total cost of materials used. Give exact answers. w = cm l = cm h = cm

Explanation / Answer

L*w*H = 540 (VOLUME IS GIVEN)

COST FOR MANUFACTURING THE BOX =

4* SIDE AREA*5 + 10*(TOP+ BOTTOM AREA)

=>> 20 wh + 10*2*lh = price -----------------------(1)

TO MINIMISE THE COST

AND d(PRICE)/dl = 0

w= 540/(l*h)

hence (1) becomes 20*540/L + 20*LH= PRICE

d(PRICE)/dl = 0

10800 / L^2 = 20*H

L^2= 540/H

HENCE W CAN BE FOUND OUT FROM L*W*H =540

WHERE H= 540/L^2

HNCE W= 540* l

hence we need one more wquation as we have found out the value with respect to other variables

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