Formulate the following word problem as a linear programming problem. (Note that the natural constraints > 0, y 2 0, z > 0, have been omitted from the answers.) Do not attempt to solve it! The Flustard is an animal that eats three foods: squerps, fleebs, and blurds. A squerp costs $8 and provides 26 mg (milligrams) of mertle, 15 mg of perkle, and 29 mg of kerple. A fleeb costs $5 and provides 6 mg of mertle, 21 mg of perkle, and 9 kerple. A blurd costs $3 and provides 21 mg of mertle, 17 mg of perkle, and 25 mg of kerple. The Flustard needs at least 0.7 g (grams) of mertle, 1.3 g of perkle, and 1 g of kerple every day to live. What's the cheapest way to feed your pet Flustard for one day? Use the variables mg of = # squerps = # fleebs = # blurds. (Note: 1 g. = 1000 mg.) minimize 700x + 1300y + 1000z subject to the constraints minimize 8x + 5y + 3z subject to the constraints 26x + 6y + 21z > 8 15x + 21y + 17z 2 5 29x + 9y + 25z > 3 26x + 6y + 21z < 700 15x + 21y + 17z < 1300 29x + 9y + 25z < 1000 (A) (В) minimize 700x + 1300y + 1000z subject to the constraints maximize 8x+ 5y + 3z subject to the constraints 26x + 6y + 21z < 8 15x + 21y + 17z < 5 29x + 9y + 25z < 3 26x + 6y + 21lz > 700 15x + 21y + 17z > 1300 29x + 9y + 25z 2 1000 (C) (D) maximize 8x+ 5y + 3z maximize 700x+ 1300y+ 1000z subject to the constraints subject to the constraints 26x + 6y + 21z < 8 15x + 21y + 17z < 5 29x + 9y + 25z < 3 26x + 6y + 21z < 700 15x + 21y + 17z < 1300 29x + 9y + 25z < 1000 (E) (F) maximize 700x+1300y+ 1000z subject to the constraints minimize 8x+ 5y + 3z subject to the constraints 26x + 6y + 21z > 8 15x + 21y + 17z > 5 29x + 9y + 25z 2 3 26x + 6y + 21z > 700 15x + 21y + 17z > 1300 29x + 9y + 25z > 1000 (G) (H)
Formulate the following word problem as a linear programming problem. (Note that the natural constraints > 0, y 2 0, z > 0, have been omitted from the answers.) Do not attempt to solve it! The Flustard is an animal that eats three foods: squerps, fleebs, and blurds. A squerp costs $8 and provides 26 mg (milligrams) of mertle, 15 mg of perkle, and 29 mg of kerple. A fleeb costs $5 and provides 6 mg of mertle, 21 mg of perkle, and 9 kerple. A blurd costs $3 and provides 21 mg of mertle, 17 mg of perkle, and 25 mg of kerple. The Flustard needs at least 0.7 g (grams) of mertle, 1.3 g of perkle, and 1 g of kerple every day to live. What's the cheapest way to feed your pet Flustard for one day? Use the variables mg of = # squerps = # fleebs = # blurds. (Note: 1 g. = 1000 mg.) minimize 700x + 1300y + 1000z subject to the constraints minimize 8x + 5y + 3z subject to the constraints 26x + 6y + 21z > 8 15x + 21y + 17z 2 5 29x + 9y + 25z > 3 26x + 6y + 21z < 700 15x + 21y + 17z < 1300 29x + 9y + 25z < 1000 (A) (В) minimize 700x + 1300y + 1000z subject to the constraints maximize 8x+ 5y + 3z subject to the constraints 26x + 6y + 21z < 8 15x + 21y + 17z < 5 29x + 9y + 25z < 3 26x + 6y + 21lz > 700 15x + 21y + 17z > 1300 29x + 9y + 25z 2 1000 (C) (D) maximize 8x+ 5y + 3z maximize 700x+ 1300y+ 1000z subject to the constraints subject to the constraints 26x + 6y + 21z < 8 15x + 21y + 17z < 5 29x + 9y + 25z < 3 26x + 6y + 21z < 700 15x + 21y + 17z < 1300 29x + 9y + 25z < 1000 (E) (F) maximize 700x+1300y+ 1000z subject to the constraints minimize 8x+ 5y + 3z subject to the constraints 26x + 6y + 21z > 8 15x + 21y + 17z > 5 29x + 9y + 25z 2 3 26x + 6y + 21z > 700 15x + 21y + 17z > 1300 29x + 9y + 25z > 1000 (G) (H)
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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Transcribed Image Text:Formulate the following word problem as a linear programming problem. (Note that
the natural constraints r > 0, y 2 0, z 2 0, have been omitted from the answers.) Do
not attempt to solve it!
The Flustard is an animal that eats three foods: squerps, fleebs, and blurds. A squerp
costs $8 and provides 26 mg (milligrams) of mertle, 15 mg of perkle, and 29 mg of
kerple. A fleeb costs $5 and provides 6 mg of mertle, 21 mg of perkle, and 9 mg of
kerple. A blurd costs $3 and provides 21 mg of mertle, 17 mg of perkle, and 25 mg of
kerple. The Flustard needs at least 0.7 g (grams) of mertle, 1.3 g of perkle, and 1 g of
kerple every day to live. What's the cheapest way to feed your pet Flustard for one
day? Use the variables
# squerps
= # fleebs
= # blurds.
(Note: 1 g. = 1000 mg.)
minimize 700x + 1300y + 1000z
subject to the constraints
minimize 8x+ 5y + 3z
subject to the constraints
26x + 6y + 21z > 8
15x + 21y + 17z > 5
29x + 9y + 25z > 3
26x + 6y + 21z < 700
15x + 21y + 17z < 1300
29x + 9y + 25z < 1000
(A)
(B)
minimize 700x + 1300y + 1000z
subject to the constraints
maximize 8x + 5y + 3z
subject to the constraints
26x + 6y + 21z < 8
15x + 21y + 17z < 5
29x + 9y + 25z < 3
26x + 6y + 21lz > 700
15x + 21y + 17z > 1300
29x + 9y + 25z > 1000
(D)
maximize 700x+ 1300y+ 1000z
subject to the constraints
+ 5y + 3z
subject to the constraints
maximize
26x + 6y + 21z < 8
15x + 21y + 17z < 5
29x + 9y + 25z < 3
26x + 6y + 21z < 700
15x + 21y + 17z < 1300
29x + 9y + 25z < 1000
(E)
(F)
maximize 700r+1300y+ 1000z
minimize 8x+5y + 3z
subject to the constraints
subject to the constraints
26x + 6y + 21z > 8
15x + 21y + 17z > 5
29x + 9y + 25z 2 3
26x + 6y + 21lz > 700
15x + 21y + 17z 2 1300
29x + 9y + 25z > 1000
(H)
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