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MaRussiya [10]
3 years ago
9

Solve and show work.

Mathematics
1 answer:
Elan Coil [88]3 years ago
8 0
A) to get the profit to equal to 0
-x^2+6x+432=0
divide all by -1 to get rid of the negative in front
x^2-6x-432=0
factor
(x-24)(x+18)=0
x=21,-18
can’t sell -18 items so the answer is
24 ITEMS

b)maximize the profits meaning the maximum points aka. the VERTEX (where the graph is at its highest)
using x=-b/2a formula
you get x=3
to maximize the profit, they need to sell 3 items
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See attached. (Both inequalities graph to the same region.)

Step-by-step explanation:

To graph an inequality, you first replace the inequality symbol by an equal sign. Then you graph the line (or curve) described by the equation. If the inequality symbol includes the "or equal to" case, then the line (or curve) is solid and is part of the solution set. If not, then the line (or curve) is dashed and is <em>not part of the solution set</em>.

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Note that the line -x -y = -5 (from the second inequality) is the same ilne.

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After you have graphed the boundary of the solution region, you need to determine which side of the boundary has the solutions. I find it easy to do this by locating an x- or y-term with a positive coefficient and seeing which side of the inequality symbol that lies on. Here, both the x-term and the y-term lie on the "is greater than" side of the symbol, so the half-plane is shaded above and to the right of the line, where x- and y-values are greater than they are on the line.

In the second inequality, you can multiply the whole thing by -1 to get

... x + y > 5 . . . . same as the first inequality

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Once again, the x- and y-values that satisfy this are greater than those that are on the boundary line.

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The graph seems to show only one equation. Both are there, but the dashed blue line sits on top of the dashed red line, so you can't see it. The purple shading indicates both red and blue shading in the same area.

===== =====

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