(a) Make a contour diagram of a standard baseball with the diameter of 73mm show
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Question
(a) Make a contour diagram of a standard baseball with the diameter of 73mm show at least 10 contours.
(b) A company makes three types of cookies: shortbread, mint, and fudge swirl. The cost of producing s pounds of shortbread, m pounds of mint, and f pounds of fudge swirl is given by C=s+2m+3f in dollars. Sketch the portion of the level surface C=12 that lies in the first octant. (Label your 3 axes with s,m,f, and start by finding the s,m,and f intercepts). What is the significance of the level surface you drew in part (b)?
Explanation / Answer
A function of 3 variables is a function of the form U(x,y,z) whose inputs are points in R3 and whose outputs are numbers. For example, U( x,y,z) = x2yz is a function of 3 variables. In this section, we generalize many of the concepts from chapter 10 to concepts involving functions of 3 variables. Given a function of 3 variables U( x,y,z) , we define the level surface of U( x,y,z) of level k to be the set of all points in R3 which are solutions to U( x,y,z) = k Indeed, many of the most familiar surfaces are level surfaces of functions of 3 variables.
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