It’s a problem with three questions, please answer them a. b. c. Be clear 10. A florist sells candles and vases. There must be at least 5 items in each shipment, but there cannot be morethan 12 in a shipment. Additionally, the shipment must weigh less than 35 pounds. Each shipment containerweighs 5 pounds, plus 2 pounds of packing material. A candle weighs 3 pounds and a vase weighs 1.5 pounds.a) Write a system of inequalities to represent the constraints on the number of items that can be included in oneshipment.b) Suppose that John wants to buy 12 candles. Would he be able to get them all in one shipment? Explain howyou determined your answer.c) Suppose Mary wants to buy 6 candles and 6 vases. Would she be able to get them all in one shipment?Explain how you determined your answer.

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Description: It’s a problem with three questions, please answer them a. b. c. Be clear 10. A florist sells candles and vases. There must be at least 5 items in each shipment, but there cannot be morethan 12 in a shipment. Additionally, the shipment must weigh les

Answered: 10. A florist sells candles and vases.…

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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It’s a problem with three questions, please answer them a. b. c. Be clear

10. A florist sells candles and vases. There must be at least 5 items in each shipment, but there cannot be more
than 12 in a shipment. Additionally, the shipment must weigh less than 35 pounds. Each shipment container
weighs 5 pounds, plus 2 pounds of packing material. A candle weighs 3 pounds and a vase weighs 1.5 pounds.
a) Write a system of inequalities to represent the constraints on the number of items that can be included in one
shipment.
b) Suppose that John wants to buy 12 candles. Would he be able to get them all in one shipment? Explain how
you determined your answer.
c) Suppose Mary wants to buy 6 candles and 6 vases. Would she be able to get them all in one shipment?
Explain how you determined your answer.

Expert Solution

Step 1

let x be the number of candles and y be the number of vases.

since there must be at least 5 items in the shipment , therefore, $x + y \geq 5$

there can not be more than 12 items in the shipment , therefore, $x + y \leq 12$

combining we get

$5 \leq x + y \leq 12$

weight of 1 candles is 3 pounds and weight of 1 vases is 1.5 pounds .

therefore, total weight of x candles and y vases is given by $3 x + 1.5 y$

weight of the shipment must be less than 35 pounds, therefore, $3 x + 1.5 y + 5 + 2 \leq 35$ where 5 pounds is the weight of the shipment container and 2 pounds is weight of packing material .

(a)

the system of inequalities is given by $5 \leq x + y \leq 12$

$3 x + 1.5 y + 5 + 2 \leq 35$

Step 2

(b) to check whether John will be able to get the 12 candles in one shipment , substitute $x = 12$ and $y = 0$ in the inequalities .

$5 \leq 12 + 0 \leq 12$ gives $5 \leq 12 \leq 12$ which is true.

check the second inequality

$\begin{array}{rcl} 3 (12) + 1.5 (0) + 5 + 2 & \leq & 35 \\ 43 & \leq & 35 \end{array}$

which is false.

Hence John will not be able to receive 12 candles in 1 shipment.

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