10 Question 4 (4 points) For their Christmas collection, a chocolate factory is going to use closed boxes in the form of decorated houses, with a content of 960 cm³. The dimensions of the house are given below, in terms of two variables x and y (in cm). 5x y 5x 6x 9x 6x 8x y y For the front and the back, a material will be used that costs 2 eurocent per cm², for all other sides the material costs 1 eurocent per cm². a) Show that the total cost C for the box (in eurocent) as a function of x is given by C = 240x² + 480 Χ You may use that the volume of the box is given by 60x2y (you do not have to show this). b) Find the values of x and y so that the cost for the box is minimal. What is the minimum cost?
10 Question 4 (4 points) For their Christmas collection, a chocolate factory is going to use closed boxes in the form of decorated houses, with a content of 960 cm³. The dimensions of the house are given below, in terms of two variables x and y (in cm). 5x y 5x 6x 9x 6x 8x y y For the front and the back, a material will be used that costs 2 eurocent per cm², for all other sides the material costs 1 eurocent per cm². a) Show that the total cost C for the box (in eurocent) as a function of x is given by C = 240x² + 480 Χ You may use that the volume of the box is given by 60x2y (you do not have to show this). b) Find the values of x and y so that the cost for the box is minimal. What is the minimum cost?
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question 4 (4 points)
For their Christmas collection, a chocolate factory is going to use closed boxes in the form of
decorated houses, with a content of 960 cm³. The dimensions of the house are given below, in terms
of two variables x and y (in cm).
5x
y
5x
6x
9x
6x
8x
y
y
For the front and the back, a material will be used that costs 2 eurocent per cm², for all other sides
the material costs 1 eurocent per cm².
a) Show that the total cost C for the box (in eurocent) as a function of x is given by
C = 240x² +
480
Χ
You may use that the volume of the box is given by 60x2y (you do not have to show this).
b) Find the values of x and y so that the cost for the box is minimal. What is the minimum cost?
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