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matrenka [14]
3 years ago
15

A builder makes a certain type of concrete by mixing together 1 part portland cement (made from lime and clay), 3 parts sand, an

d 5 parts crushed stone. If 765 ft^3 of concrete are needed, how many cubic feet of each ingredient does he need?
​
Mathematics
1 answer:
Mariana [72]3 years ago
3 0

Answer:

  • 85 ft^3 portland cement
  • 255 f^3 sand
  • 425 ft^3 crushed stone

Step-by-step explanation:

The total number of parts is 1+3+5 = 9. The relevant fractions of the mix are ...

  1/9 = portland cement

  3/9 = 1/3 = sand

  5/9 = crushed stone

Since the total is 765 ft^3, the ingredients required are ...

  (1/9)(765 ft^3) = 85 ft^3 portland cement

  (1/3)(765 ft^3) = 255 f^3 sand

  (5/9)(765 ft^3) = 425 ft^3 crushed stone

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3 years ago
A manufacturer produces two types of bottled coffee drinks: cappuccinos and cafés au lait. Each bottle of cappuccino requires 6
OlgaM077 [116]

Answer:

  • <u><em>P = 0.40x + 0.50y</em></u>

Explanation:

The <em>objective function</em> is the function that you want to optimize: usually minimize in the case of costs, and maximize in the case of revenues or profits.

In this case, you know the <em>profits</em> that a manufacturer earns from two types of <em>bottled coffe drinks</em>: <em>cappuccinos</em> and <em>cafés au lait</em>.

Each bottle of <em>cappuccino earns a profit of $0.40</em> and each bottle of <em>café au lait earns a profit of $0.50</em>.

Then:

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The total profit earned, P, is the sum of the profits earned from each type of bottled coffee drinks:

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That is the <em>objective function</em>, i.e. the function that the manufacturer must try to maximize subject to the corresponding constraints.

7 0
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