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seropon [69]
2 years ago
14

A company sells widgets. The amount of profit, y, made by the company, is related to the selling price of each widget, x, by the

given equation. Using this equation, find out the maximum amount of profit the company can make, to the nearest dollar. y=-2x^2+105x-859 y=−2x 2 +105x−859
Mathematics
1 answer:
nalin [4]2 years ago
8 0

Answer:

$519

Step-by-step explanation:

Given the amount of profit made expressed as y=-2x^2+105x-859

At maximum profit, dy/dx = 0

dy/dx = -4x + 105

0 = -4x + 105

4x = 105

x = 105/4

x = 26.25

Substitute into the original function

y=-2x^2+105x-859

y=-2(26.25)^2+105(26.25)-859

y = - 1,378.125+2,756.25-859

y = 519.125

Hence the maximum amount of profit the company can make is $519

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The question incomplete without specifying what we are to determine.

Question:A builder is buying property where she can build new houses. The line plot shows the sizes for each house. 1/6 has 6 X's 1/3 has 3 X's and 1/2 has 6 X's. Organize the information in a line plot. What is the average size of the lots? _________ acre

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Solution:

We are asked to organize the information in a line plot. See attachment for the line plot.

Given: 1/6 has 6 X's 1/3 has 3 X's and 1/2 has 6 X'sIn no particular order, the sizes of the lots are:1/6, 1/6, 1/6, 1/6, 1/6, 1/6, 1/3, 1/3, 1/3, 1/2, 1/2, 1/2, 1/2, 1/2 and 1/2 acre.

Let's count the number of lot for each size given.

For 1/6: there are 6 X's on the line plot of 1/6 number of lot for 1/6

= the lot × number of times it occurs

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For 1/3: there are 3 X's on the line plot of 1/3 number of lot for 1/3 = the lot × number of times it occurs

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The total number of lots given = 15

Average size of the lots = 5/15 = 1/3

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