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hoa [83]
2 years ago
9

Deluxe River Cruises operates a fleet of river vessels. The fleet has two types of vessels: A type-A vessel has 60 deluxe cabins

and 160 standard cabins, whereas a type-B vessel has 80 deluxe cabins and 120 standard cabins. Under a charter agreement with Odyssey Travel Agency, Deluxe River Cruises is to provide Odyssey with a minimum of 360 deluxe and 680 standard cabins for their 15-day cruise in May. It costs $42,000 to operate a type-A vessel and $51,000 to operate a type-B vessel for that period. How many of each type of vessel (x type-A and y type-B) should be used in order to keep the operating costs to a minimum
Mathematics
1 answer:
bixtya [17]2 years ago
8 0

Answer: It should be used 2 for type-A and 3 for type-B to minimize the cost.

Step-by-step explanation: As it is stipulated, <u>x</u> relates to type-A and y to type-B.

Type-A has 60 deluxe cabins and B has 80. It is needed a minimum of 360 deluxe cabins, so:

60x + 80y ≤ 360

For the standard cabin, there are in A 160 and in B 120. The need is for 680, so:

160x + 120y ≤ 680

To calculate how many of each type you need:

60x + 80y ≤ 360

160x + 120y ≤ 680

Isolating x from the first equation:

x = \frac{360 - 80y}{60}

Substituing x into the second equation:

160(\frac{360 - 80y}{60}) + 120y = 680

-3200y+1800y = 10200 - 14400

1400y = 4200

y = 3

With y, find x:

x = \frac{360 - 80y}{60}

x = \frac{360 - 80.3}{60}

x = 2

To determine the cost:

cost = 42,000x + 51,000y

cost = 42000.2 + 51000.3

cost = 161400

To keep it in a minimun cost, it is needed 2 vessels of Type-A and 3 vessels of Type-B, to a cost of $161400

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A number and another number which is 3 times 1 less than the first number add to 17. what are the numbers?
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The obtained two numbers by substitution method are 5 and 12.

<h3>What is substitution method?</h3>

The algebraic method for solving simultaneous linear equations is the substitution method.

  • The value of one variable through one equation is substituted in the second equation, as the name implies.
  • To verify an equation system by substitution, enter your x and y values into the initial equations.
  • Your answer is accurate if both simplification expressions are true.

Let the first number be 'x'.

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From the given condition that second number is 3 times 1 less than the first number.

That is;

y = 3(x - 1)

Now the sum of both number are given as 17.

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Use substitution method, and put the value of y in the total sum.

x + y = 17.

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Put the value of x in y to find the value.

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Therefore, the values of two numbers are 5 and 12.

To know more about the substitution method, here

brainly.com/question/22340165

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