Answered: 4.manufactures 37-in. high def LCD tvs…

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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Question

3.3

4.manufactures 37-in. high def LCD tvs in 2 separate locations, Locations I and II. The output at Location I is at most 6000 televisions/month, whereas the output at Location II is at most 5000 televisions/month. TMA is the main supplier of tvs to the Pulsar Corporation, its holding company, which has priority in having all its requirements met. In a certain month, Pulsar placed orders for 3000 and 4000 televisions to be shipped to two of its factories located in City A and City B, respectively. The shipping costs (in dollars) per television from the 2 TMA plants to the 2 Pulsar factories are as follows.

	To Pulsar Factories
From TMA	City A	City B
Location I	$7	$3
Location II	$8	$9

TMA will ship x televisions from Location I to city A and y televisions from Location I to city B. Find a shipping schedule that meets the requirements of both companies while keeping costs to a minimum.

(x,y)=

What is the minimum cost?

6.Solve the linear programming problem by the method of corners.

Maximize	P = x + 2y
	x	+	y	≤	4
	2x	+	y	≤	7
	x ≥ 0, y ≥ 0

The maximum is P = at

(x, y) =

Minimize	C = 2x + 6y
subject to	x	+	y	≥	3
	x	+	2y	≥	5
	x ≥ 0, y ≥ 0

The minimum is C = at

(x, y) =

10.Aerobics manufactures 2 models of steppers used for aerobic exercises, x number of luxury models and y number of standard models. Manufacturing each luxury model requires 10 lb of plastic and 10 min of labor. Manufacturing each standard model requires 16 lb of plastic and 8 min of labor. The profit for each luxury model is $45, and the profit for each standard model is $30. If 6000 lb of plastic and 60 labor-hours are available for the production of the steppers per day, how many steppers of each model should Bata produce each day in order to maximize its profit?

(x, y)

What is the optimal profit?
$

Maximize	P = 4x + 7y
subject to	2x	+	3y	≤	12
	x	+	y	≤	5
	x ≥ 0, y ≥ 0

The maximum is P = at

(x, y) =

Maximize	P = 6x + 7y
subject to	2x	+	y	≤	12
	x	−	2y	≤	1
	x ≥ 0, y ≥ 0

The maximum is P = at

(x, y)

Minimize	C = 5x + 6y
subject to	x	+	3y	≥	15
	4x	+	y	≥	16
	x ≥ 0, y ≥ 0

The minimum is C = at

(x, y)

Maximize	P = 6x + 4y
subject to	x	+	2y	≤	14
	x	+	y	≤	8
	2x	−	3y	≥	6
	x ≥ 0, y ≥ 0

The maximum is P = at

(x, y)

Minimize	C = 5x + 7y
subject to	3x	+	5y	≥	45
	3x	+	10y	≥	60
	x ≥ 0, y ≥ 0

The minimum is C = at

(x, y)

Find the maximum and minimum of Q = 2x + 6y subject to

x	+	y	≥	4
−x	+	y	≤	6
x	+	3y	≤	30
		x	≤	15
x ≥ 0, y ≥ 0.

The minimum is P = at

(x, y) =
9

Manufacturing has a division that produces x model A grates and y model B grates. To produce each model A grate requires 3 lb of cast iron and 6 min of labor. To produce each model B grate requires 4 lb of cast iron and 3 min of labor. The profit for each model A grate is $1.00, and the profit for each model B grate is $3.50. Available for grate production each day are 1000 lb of cast iron and 20 labor-hours. Because of a backlog of orders for model B grates, the manager has decided to produce at least 180 model B grates per day. How many grates of each model should they produce to maximize its profits?

(x, y)

What is the optimal profit?
$

The maximum is P = at

(x, y) =

A manufacturer of projection TVs must ship a total of at least 1000 TVs to its two central warehouses, x to the first warehouse and y to the second warehouse. Each warehouse can hold a maximum of 750 TVs. The first warehouse already has 150 TVs on hand, whereas the second has 50 TVs on hand. It costs $8 to ship a TV to the first warehouse, and it costs $18 to ship a TV to the second warehouse. How many TVs should be shipped to each warehouse to minimize cost?

(x, y)

What is the minimum cost?
$

5.1

Dav owns $20,000 worth of 10-year bonds of Ace Corporation. These bonds pay interest every 6 months at the rate of 2%/year (simple interest). How much income will Dav receive from this investment every 6 months?
$
How much interest will Dav receive over the life of the bonds?
$

Find the simple interest on a $1400 investment made for 5 years at an interest rate of 6%/year. What is the accumulated amount? (Round your answers to the nearest cent.)

simple interest	$
accumulated amount	$

Find the effective rate corresponding to the given nominal rate. (Use a 365-day year.)

4%/year compounded semiannually

%/year

Find the effective rate of interest corresponding to a nominal rate of 3.8%/year compounded annually, semiannually, quarterly, and monthly. (Round your answers to two decimal places.)

annually	%
semiannually	%
quarterly	%
monthly	%

Determine the simple interest rate at which $2400 will grow to $2571 in 9 months. (Round 2 decimal places.)
%/year

How many days will it take for $1900 to earn $12 interest if it is deposited in a bank paying simple interest at the rate of 4%/year? (365-day. Round nearest full day.)

days

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