TMA manufactures 37-in. high definition LCD televisions in two 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 televisions 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 per television from the two TMA plants to the two Pulsar factories are as follows. To Pulsar Factories From TMACity ACity B Location I$7$3 Location II$8$9TMA will ship x televisions from Location I to city A and y televisions from Location I to city B. Find a shipping schedule that meets the requirements of both companies while keeping costs to a minimum.(x, y)$=Solve the linear programming problem by the method of corners.MaximizeP = x + 2y subject to x + y ≤4 2x + y ≤7 x ≥ 0, y ≥ 0The maximum is P = at (x, y) = Bata Aerobics manufactures two 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 $30. If 6000 lb of plastic and 60 labor-hours are available for the production of the steppers per day, how many steppers of each model should Bata produce each day in order to maximize its profit?(x, y) = What is the optimal profit?$ Solve the linear programming problem by the method of corners.MinimizeC = 2x + 6ysubject to x + y ≥3 x + 2y ≥5 x ≥ 0, y ≥ 0The minimum is C = at (x, y) =David owns $20,000 worth of 10-year bonds of Ace Corporation. These bonds pay interest every 6 months at the rate of 2%/year (simple interest). How much income will David receive from this investment every 6 months?$ How much interest will David 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 %/yearFind 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 your answer to two decimal places.) %/yearHow 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? (Use a 365-day year. Round your answer up to the nearest full day.) daysHaving received a large inheritance, Jing-mei's parents wish to establish a trust for her college education. Nine years from now they need an estimated $150,000. How much should they set aside in trust now if they invest the money at 6.2%/year compounded quarterly? Continuously? (Round your answers to the nearest cent.)quarterly$ continuously$ Find the accumulated amount after 5 years if $4000 is invested at 2%/year compounded continuously. (Round your answer to the nearest cent.)$ A bank deposit paying simple interest at the rate of 8%/year grew to $2000 in 10 months. Find the principal. (Round your answer to the nearest cent.)$ Use logarithms to solve the problem.How long will it take an investment of $3000 to triple if the investment earns interest at the rate of 3%/year compounded daily? (Round your answer to two decimal places.) yrA beneficiary of a trust fund established for him 16 years ago at his birth. If the original amount placed in trust was $50,000, how much will he receive if the money has earned interest at the rate of 9%/year compounded annually? Compounded quarterly? Compounded monthly? (Round your answers to the nearest cent.)compounded annually $ compounded quarterly $ compounded monthly $ Find the accumulated amount at the end of 10 months on a $1200 bank deposit paying simple interest at a rate of 9%/year. (Round your answer to the nearest cent.)$ A bank deposit paying simple interest grew from an initial amount of $1000 to $1050 in 6 months. Find the interest rate. %/yearFind the accumulated amount A if the principal P is invested at the interest rate of r/year for t years.P = $2500, r = 5%, t = 1312, compounded semiannuallyA = $ 7.5, Chris invested $10,000 in a retirement fund that grew at the rate of 2.82%/year compounded quarterly. What is his account worth today? P = $210,000, r = 2.5%, t = 3, compounded daily, A=$

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Description: TMA manufactures 37-in. high definition LCD televisions in two 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 su

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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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TMA manufactures 37-in. high definition LCD televisions in two 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 televisions 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 per television from the two TMA plants to the two 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)

Solve the linear programming problem by the method of corners.

Maximize P = x + 2y

subject to   x + y ≤ 4

2x + y ≤ 7

x ≥ 0, y ≥ 0

The maximum is P =  at
(x, y) =
- - Bata Aerobics manufactures two 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?
    $ Solve the linear programming problem by the method of corners.
    
    Minimize C = 2x + 6y
    
    subject to   x + y ≥ 3
    
    x + 2y ≥ 5
    
    x ≥ 0, y ≥ 0
    
    The minimum is C =   at
    (x, y) =
  - David 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 David receive from this investment every 6 months?
    $
    
    How much interest will David 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 your answer to two 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? (Use a 365-day year. Round your answer up to the nearest full day.)
    
    days
  - Having received a large inheritance, Jing-mei's parents wish to establish a trust for her college education. Nine years from now they need an estimated $150,000. How much should they set aside in trust now if they invest the money at 6.2%/year compounded quarterly? Continuously? (Round your answers to the nearest cent.)
    
    quarterly$ continuously$
  - Find the accumulated amount after 5 years if $4000 is invested at 2%/year compounded continuously. (Round your answer to the nearest cent.)
    $
  - A bank deposit paying simple interest at the rate of 8%/year grew to $2000 in 10 months. Find the principal. (Round your answer to the nearest cent.)
    
    $
  - Use logarithms to solve the problem.
    How long will it take an investment of $3000 to triple if the investment earns interest at the rate of 3%/year compounded daily? (Round your answer to two decimal places.)
    yr
  - A beneficiary of a trust fund established for him 16 years ago at his birth. If the original amount placed in trust was $50,000, how much will he receive if the money has earned interest at the rate of 9%/year compounded annually? Compounded quarterly? Compounded monthly? (Round your answers to the nearest cent.)
    
    compounded annually     $
    
    compounded quarterly     $
    
    compounded monthly     $
  - Find the accumulated amount at the end of 10 months on a $1200 bank deposit paying simple interest at a rate of 9%/year. (Round your answer to the nearest cent.)
    $
  - A bank deposit paying simple interest grew from an initial amount of $1000 to $1050 in 6 months. Find the interest rate.
    
    %/year
  - Find the accumulated amount A if the principal P is invested at the interest rate of r/year for t years.
    
    P = $2500, r = 5%, t = 13
    
    1
    
    2
    
    ,
    compounded semiannually
    
    A = $
  - 7.5, Chris invested $10,000 in a retirement fund that grew at the rate of 2.82%/year compounded quarterly. What is his account worth today?
  - P = $210,000,
    r = 2.5%,
    t = 3, compounded daily, A=$

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

compounded annually	$
compounded quarterly	$
compounded monthly	$

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

Solve the linear programming problem by the method of corners. Maximize P = x + 2y subject to x + y ≤ 4 2x + y ≤ 7 x ≥ 0, y ≥ 0