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Vinvika [58]
3 years ago
6

You plan to make a series of deposits in an interest-bearing account. You will deposit $1,000 today, $2,000 in 2 years, and $8,0

00 in 5 years. If you withdraw $3,000 in 3 years and $5,000 in 7 years, how much will you have after eight years if the interest rate is 9%?
Business
1 answer:
solniwko [45]3 years ago
7 0

Answer:

$5,641

Explanation:

DEPOSIT NOW  

$1000 * FVIF 9%,8 PERIODS

= $1000 * 1.9926

= $1992.6

IN 2 YEARS

= $2000 * FVIF 9%,6 PERIODS

= $2000 * 1.6771

= $3354.20

IN 5 YEARS

= $8000 * FVIF 9%, 3 PERIODS

= $8000*1.2950

= $10360

WITHDRAWAL: IN 3 YEARS

= ($3000) * FVIF 9%, 5 PERIODS

= ($3000) * 1.5386

= ($4615.80)

IN 7 YEARS

= ($5000) * FVIF 9%, 1 PERIOD

= ($5000) * 1.0900

= ($5450)

Total value = $1992.6  + $3354.20 + $10360  - $4615.80 - $5450

Total value = $5,641

So, the total future value after eight years is $5,641

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Answer:

(a) Linear model

max\ P = 9x + 7y

Subject to:

12x + 4y \le 60

4x + 8y \le 40

x,y \ge 0

(b) Standard form:

max\ P = 9x + 7y

Subject to:

12x + 4y + s_1 = 60

4x + 8y +s_2= 40

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Explanation:

Given

\begin{array}{ccc}{} & {Hours/} & {Unit} & {Product} & {Line\ 1} & {Line\ 2} & {A} & {12} & {4} & {B} & {4} & {8} & {Total\ Hours} & {60} &{40}\ \end{array}

Solving (a): Formulate a linear programming model

From the question, we understand that:

A has a profit of $9 while B has $7

So, the linear model is:

max\ P = 9x + 7y

Subject to:

12x + 4y \le 60

4x + 8y \le 40

x,y \ge 0

Where:

x \to line\ 1

y \to line\ 2

Solving (b): The model in standard form:

To do this, we introduce surplus and slack variable "s"

For \le inequalities, we add surplus (add s)

Otherwise, we remove slack (minus s)

So, the standard form is:

So, the linear model is:

max\ P = 9x + 7y

Subject to:

12x + 4y + s_1 = 60

4x + 8y +s_2= 40

x,y \ge 0

s_1,s_2 \ge 0

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Answer:

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When an isocost line is tangent to an isoquant cost is being minimized

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