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matrenka [14]
2 years ago
6

. A company produces two products, A and B, which have profits of $9 and $7, respectively. Each unit of product must be processe

d on two assembly lines, where the required production times are as follows. Product Hours/Unit Line 1 Line 2 A 12 4 B 4 8 Total hours 60 40 a) Formulate a linear programming model to determine the optimal product mix that will maximize profit. b) Transform this model into standard form.
Business
1 answer:
prohojiy [21]2 years ago
4 0

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

x,y \ge 0

s_1,s_2 \ge 0

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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Dennis_Churaev [7]

Answer:

current price = $1191.79

Explanation:

given data

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maturity time  = 14 year

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solution

we get here first annual coupon rate = 7.5% of 1000

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current price of the bonds = \frac{C}{(1+r)} +\frac{C}{(1+r)^2} +\frac{C}{(1+r)^3} +\frac{C}{(1+r)^4} ..........\frac{C}{(1+r)^{13}} + \frac{C+par\ value}{(1+r)^{14}}      .................1

put here value

current price = \frac{75}{(1+r)} +\frac{75}{(1+r)^2} +\frac{75}{(1+r)^3} +\frac{75}{(1+r)^4} ..........\frac{75}{(1+r)^{13}} + \frac{75+1000}{(1+r)^{14}}  

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solve it we get

current price = $1191.79

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3 years ago
If total liabilities decreased by $15,000 and stockholders' equity increased by $10,000 during a period of time, then total asse
scoray [572]

Answer:

The total assets must change by B) $5,000 decrease

Explanation:

hi, remember that:

Assets=Liabilities+Equity

If liabilities decrease by $15,000 and equity increases by $10,000...

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Assets=Liabilities+Equity-5,000

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almond37 [142]

An effective Boolean search strategy that Magda should adopt is the use of Boolean operators and emboldened keywords.

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Del is buying a $250,000 home. He has been approved for a 5.75% mortgage. He was required to make a 15% down payment and will be
alukav5142 [94]

Answer:

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Explanation:

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