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AnnZ [28]
2 years ago
14

2. Max z = 3X1 + 5X2+ 4X3 S.t.2X1 +3X2 ≤ 18 2X1 + X2 ≤ 10 3X1 + 2X+4X3 ≤ 15 X1, X2, X3 ≥ 0

Business
1 answer:
lions [1.4K]2 years ago
7 0

The interpretation of the result is that the maximum value of the objective function is 29

<h3>How to solve and interpret the result?</h3>

The objective function is given as:

Max z = 3x₁ + 5x₂+ 4x₃

The constraints are:

2x₁ +3x₂ ≤ 18

2x₁ + x₂ ≤ 10

3x₁ + 2x₂ +4x₃ ≤ 15

x₁, x₂, x₃ ≥ 0

Subtract the second inequality from the first

2x₁ - 2x₁ + 3x₂ - x₂ ≤ 18 - 10

Evaluate the like terms

2x₂ ≤ 8

Divide by 2

x₂ ≤ 4

Substitute 4 for x₂ in 2x₁ +3x₂ ≤ 18

2x₁ +3*4 ≤ 18

This gives

2x₁ + 12 ≤ 18

Evaluate the like terms

2x₁ ≤ 6

Divide by 2

x₁ ≤ 3

Substitute 4 for x₂ and 3 for x₁ in 3x₁ + 2x₂ +4x₃ ≤ 15

3*3 + 2*4 +4x₃ ≤ 15

This gives

17 +4x₃ ≤ 15

Evaluate the like terms

4x₃ ≤ -2

Divide by 4

x₃ ≤ -0.5

From the constraints, we have:

x₁, x₂, x₃ ≥ 0

So, we set all negative values to 0

This means that:

x₃ ≤ 0

Substitute these values in the objective function

Max z = 3 * 3 + 5 * 4 + 4 * 0

Evaluate

Max z = 29

Hence, the interpretation of the result is that the maximum value is 29

Read more about objective functions at:

brainly.com/question/11206462

#SPJ1

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Gramps purchased a joint survivor annuity that pays $500 monthly over his remaining life and that of his wife, Gram. Gramps is 7
Bezzdna [24]

Answer:

$150

Explanation:

Calculation of how much income that Gramps will recognize on the first payment.

Since joint survivor annuity has 23.1 as the annual return multiple .

Calculation for Expected return

Expected return =Annual payment *Return multiple

($500*12) =$6,000

$6,000×23.1

=$138,600

Therefore :

$97,020/$138,600

=0.7×100

=70%

The 70% of each of the payment will be the return of capital while the 30%(100%-70%) will be the income.

Hence the first payment be:

30%×500

=$150

Therefore the amount of income that Gramps will recognize on the first payment will be $150

6 0
3 years ago
Suppose that Omar's marginal utility for each additional cup of coffee is 5.5 utils per cup no matter how many cups he drinks. O
Lelechka [254]

Answer:

Explanation:

To answer this question, we first need to calculate the marginal utility per dollar for doughnuts. Recall that the marginal utility per dollar for a good is the marginal utility divided by the price of the good (=MU/P). For the first doughnut we have 10 (=10/$1), the second doughnut 9(=9/$1), third 9, fourth 8, fifth 7, sixth 6, seventh 5, eighth 4, ninth 3, tenth 2 and eleventh 1. The marginal utility per dollar for every cup of coffee is 5.5 (=5.5/$1). To determine how big the budget would have to be before Omar would spend a dollar buying his first cup of coffee, we compare the marginal utility per dollar values. Omar will purchase the first doughnut before he buys a cup of coffee because the marginal utility per dollar for the doughnut is greater than the marginal utility per dollar for the cup of coffee (10>1.5). The same is true for the second through the eighth doughnut. This implies Omar will buy 8 doughnuts at the price of $1 before he buys his first cup of coffee. Therefore his budget will need to $9 before he buys his first cup of coffee, $8 on the doughnuts and $1 for the cup of coffee.

Answer: $8

8 0
3 years ago
A company uses cash to pay all of the following excepta. All of these choices are correct.b. interest to creditorsc. dividends t
never [62]

Answer:

d. depreciation expense

Explanation:

The expenses which are paid by cash reduced the cash balance displayed in the balance sheet . Like interest to creditors, stockholders dividend, wages expenses, miscellaneous expenses, admin expenses, etc. These expenses can be paid either by cash or by bank account .

But the depreciation expense is a non - cash expense which reduces the fixed asset balance over the fixed asset useful life. Plus this is shown in the income statement on the debit side. Like this other examples would be goodwill impairment, amortization expenses, etc.

3 0
3 years ago
Last year, 46% of business owners gave a holiday gift to their employees. A
Liono4ka [1.6K]

Answer:

a. 15

b. Since is a left tailed test the p value would be:

p_v =P(Z<-3.263)= 0.000551

Explanation:

a. 25% of 60 businesses surveyed=

25/100 x 60= 15

b. See attached image for solution

7 0
3 years ago
Central Perk orders their organic coffee filters from a South American supplier that mails them as inexpensively (hence, as slow
Damm [24]

Answer:

1495 filters are considered as safety stock.

Explanation:

d = 80 filters, std devd= 5, L = 14 days, std dev L= 2 days

Std dev dL = Sq rt ( Lσ d2 + d 2σ L2  ) = sq rt ( 350 + 25600) = 161 filter

z= 2.33 at 99% SL

safety stock = 2.33 X 161 = 375 filter

Reorder point = dL + Safety stock = 80 X 14 + 375 = 1495 filters

3 0
3 years ago
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