Answer:
The system of inequalities would be:
L+M >= 500 (greater than or equal to)
2L + 0.5M <= 850 (less than or equal to)
The first inequality deals with the total number of balloons. She wants the total to be at least 500, so add the variables and set it greater than or equal to 500.
The second inequality deals with the helium. 2L comes from each latex balloon using 2 ft^3 of helium. 0.5M comes from each Mylar balloon using 0.5 ft^3. Together they can use no more than 85% of the 1000 ft^3 tank; 85% = 0.85; 0.85×1000=850. "No more than" tells us it must be less than or equal to
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We want to minimize s(x, y) = x + y such that xy = 36.
From the constratint we have y = 36/x, so the sum can also be written as
s(x, 36/x) = x + 36/x
Differentiate s with respect to x and find the critical points of s :
1 - 36/x² = 0 ⇒ x² = 36 ⇒ x = ±6
Both x and y must be positive, so it follows that x = y = 6, which gives a minimum sum of s(6, 6) = 12.
skunks do a warning dance, they are nocturnal, their spray is flammable, and you can fight the smell chemically.
If the long-run average total cost curve of an industry is declining at the point where it intersects the industry demand curve, then we can expect that the industry will be a natural monopoly.
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What is Natural monopoly?</h3>
This is characterized by high infrastructural costs and other barriers which prevent entry into the market. This gives rise to a very few being involved and usually offers no competition as there is a single seller with unique types of goods and services.
This type of monopoly involves sellers having a big size and able to produce the required output for the consumers. This makes them to be self-sufficient and is characterized by the long-run average total cost curve of an industry declining and intersecting the industry demand curve which is the reason why it was chosen as the most appropriate choice.
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