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math16B_solutions_assign1

# math16B_solutions_assign1 - Math 16B Section 1 Sarason...

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Math 16B, Section 1 Fall 2005 Sarason ASSIGNMENT 1 Exercise 7.1.7. Let a rectangular box have sides of length x, y, z , measured in feet, with z being the height. Suppose the material used for the top and bottom of the box costs \$3 per square foot and the material for the sides costs \$5 per square foot. Find the formula for the function C ( x, y, z ) expressing the total cost of the material in the box. Solution. The top and bottom each has area xy , so the cost for the material in each is 3 xy . There are two sides of area xz , each contributing 5 xz to the cost. There are two sides of area yz , each contributing 5 yz to the cost. The total cost is therefore given by C ( x, y, z ) = 6 xy + 10 xz + 10 yz dollars. Exercise 7.1.8. A rectangular enclosure is open at the front and has no floor. Its height is z , its front and back have length x , and its two sides have length y , all measured in feet. The material for its top costs \$3 per square foot and the material for the back and two sides costs \$5 per square foot.

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math16B_solutions_assign1 - Math 16B Section 1 Sarason...

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