Acarpenter wants to build a rectangular box with square sides in which to put round things. the material for the bottom costs $20/ft^2, material for the sides costs $10/ft^2 and the material for the top costs $50/ft^2
if the volume of the box must be 5 ft^3, then find the dimensions that will minimize the cost (and find the minimum cost).

Step-by-step explanation:

Given

Suppose side face have a dimension of l\times l

and width of h

volume

volume

Area of side wall is

Area of top Wall

Area of bottom

Cost of bottom wall

Cost of top wall

Cost of side walls

total cost

differentiate C w.r.t l to get minima or maxima

Dimension of Box is

, and

for

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote , , , so that we can call

note the following:

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from , to get to , we add

from , to get to , we add

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

, and for