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According to the shipping regulation of a company, the girth plus the length of a parcel sent by mail may not exceed 132 inches, where by "girth" we mean the perimeter of the smallest end. What is the largest possible volume of a rectangular parcel with a square end that can be sent by mail? What are the dimensions of the package of largest volume? a. Suppose a box has two square ends and other faces are rectangles. Let x represent the length of one side of the square end and y the length of the longer side. Draw the box and label the sides. b. Find a formula for the volume of the box in terms of x and y. V = c. The problem statement tells us that the parcel's girth plus length may not exceed 132 inches. In order to maximize volume, we assume that we will actually need the girth plus length to equal 132 inches. What equation does this produce involving x and y? y + 2x = 33 d. Solve the equation you found in (c) for one of x or y (whichever is easier). e. Now use your work in (b) and (d) to determine a formula for the volume of the parcel so that this formula is a function of a single variable. (Simplify your answer.) V = f. Over what domain should we consider this function? Note that both x and y must be positive; how does the constraint that girth plus length is 132 inches produce intervals of possible values for x and y? g. Find the absolute maximum of the volume of the parcel on the domain you established in (f) and hence also determine the dimensions of the box of greatest volume. , X = in, y= in, V= in3. Is/492launch type=global pavigation

According to the shipping regulation of a company, the girth plus the length of a parcel sent by mail may not exceed 132 inches, where by "girth" we mean the perimeter of the smallest end. What is the largest possible volume of a rectangular parcel with a square end that can be sent by mail? What are the dimensions of the package of largest volume? a. Suppose a box has two square ends and other faces are rectangles. Let x represent the length of one side of the square end and y the length of the longer side. Draw the box and label the sides. b. Find a formula for the volume of the box in terms of x and y. V = c. The problem statement tells us that the parcel's girth plus length may not exceed 132 inches. In order to maximize volume, we assume that we will actually need the girth plus length to equal 132 inches. What equation does this produce involving x and y? y + 2x = 33 d. Solve the equation you found in (c) for one of x or y (whichever is easier). e. Now use your work in (b) and (d) to determine a formula for the volume of the parcel so that this formula is a function of a single variable. (Simplify your answer.) V = f. Over what domain should we consider this function? Note that both x and y must be positive; how does the constraint that girth plus length is 132 inches produce intervals of possible values for x and y? g. Find the absolute maximum of the volume of the parcel on the domain you established in (f) and hence also determine the dimensions of the box of greatest volume. , X = in, y= in, V= in3. Is/492launch type=global pavigation

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
Chapter9: Surfaces And Solids
Section9.1: Prisms, Area And Volume
Problem 40E: As in Exercise 39, find the volume of the box if four congruent squares with sides of length 6 in....
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According to the shipping regulation of a company, the girth plus the length of a parcel sent by mail may not exceed 132 inches, where by "girth" we mean the perimeter of the smallest end. What is the largest possible volume of a rectangular parcel with a square end that can be sent by mail? What are the dimensions of the package of largest volume? a. Suppose a box has two square ends and other faces are rectangles. Let x represent the length of one side of the square end and y the length of the longer side. Draw the box and label the sides. b. Find a formula for the volume of the box in terms of x and y. V = yx2 c. The problem statement tells us that the parcel's girth plus length may not exceed 132 inches. In order to maximize volume, we assume that we will actually need the girth plus length to equal 132 inches. What equation does this produce involving x and y? y+ 2x = 33 d. Solve the equation you found in (c) for one of x or y (whichever is easier). e. Now use your work in (b) and (d) to determine a formula for the volume of the parcel so that this formula is a function of a single variable. (Simplify your answer.) V = f. Over what domain should we consider this function? Note that both x and y must be positive; how does the constraint that girth plus length is 132 inches produce intervals of possible values for x and y? g. Find the absolute maximum of the volume of the parcel on the domain you established in (f) and hence in, y= also determine the dimensions of the box of greatest volume. , x = in, V= in. nal tools/492launch type=global navigation
Transcribed Image Text:According to the shipping regulation of a company, the girth plus the length of a parcel sent by mail may not exceed 132 inches, where by "girth" we mean the perimeter of the smallest end. What is the largest possible volume of a rectangular parcel with a square end that can be sent by mail? What are the dimensions of the package of largest volume? a. Suppose a box has two square ends and other faces are rectangles. Let x represent the length of one side of the square end and y the length of the longer side. Draw the box and label the sides. b. Find a formula for the volume of the box in terms of x and y. V = yx2 c. The problem statement tells us that the parcel's girth plus length may not exceed 132 inches. In order to maximize volume, we assume that we will actually need the girth plus length to equal 132 inches. What equation does this produce involving x and y? y+ 2x = 33 d. Solve the equation you found in (c) for one of x or y (whichever is easier). e. Now use your work in (b) and (d) to determine a formula for the volume of the parcel so that this formula is a function of a single variable. (Simplify your answer.) V = f. Over what domain should we consider this function? Note that both x and y must be positive; how does the constraint that girth plus length is 132 inches produce intervals of possible values for x and y? g. Find the absolute maximum of the volume of the parcel on the domain you established in (f) and hence in, y= also determine the dimensions of the box of greatest volume. , x = in, V= in. nal tools/492launch type=global navigation
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