A candidate for mayor in a small town has allocated $40,000 for last-minute advertising in the days preceding the election. Two
types of ads will be used: radio and television. Each radio ad costs $200 and reaches an estimated 3,000 people. Each television ad costs $500 and reaches an estimated 7,000 people. In planning the advertising campaign, the campaign manager would like to reach as many people as possible, but she has stipulated that at least 10 ads of each type must be used. Also, the number of radio ads must be at least as great as the number of television ads. How many ads of each type should be used? How many people will this reach?Let X1= the number of radio ads purchasedX2= the number of television ads purchasedMaximize3,000X1+7,000X2(maximize exposure)Subject to:200X1+500X2≤40,000(budget constraint)X1≥10(at least 10 radio ads purchased)X2≥10(at least 10 television ads purchased)X1≥X2(# of radio ads ≥ # of television ads)X1, X2≥0(non-negativity constraints)
1 answer:
Answer:
- 175 radio ads
- 10 television ads
- 595,000 people
Step-by-step explanation:
Radio ads reach 3000/200 = 15 people per dollar.
Television ads reach 7000/500 = 14 people per dollar.
Except for the constraints on the number of TV ads, the best value for the advertising dollar comes from radio ads.
So, we must satisfy the constraint that 10 TV ads are the minimum. Then the remaining 35,000 in advertising budget can be spent on 175 radio ads. The number of people reached by this advertising will be ...
175·3000 +10·7000 = 595,000 . . . people
10 TV ads and 175 radio ads should be used. This campaign will reach 595,000 people.
_____
This graph is drawn so the feasible region is white. Areas outside the feasible region are shaded. (This approach can make identifying the feasible region easier.) The object is to get the objective function line as far from the origin as possible. The feasible region vertex (175, 10) does that.
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You basically have to find the slope, to find the average rate of change, because finding the slope and finding the average rate of change is basically the same thing.
Here's the formula :
So here, all you'd have to do is simply pick two points, and insert them into this formula. Say you take the points (-2, -2) and (0,-3). You would start from the y-intercept of the second point, and insert them all into the formula.
which would turn into 
. And so since you want a good, stable number, and not just a fraction, you would divide -1 and 2, and the average rate of change would be -0.50.
AVERAGE RATE OF CHANGE : -0.50
Here's the formula :
So here, all you'd have to do is simply pick two points, and insert them into this formula. Say you take the points (-2, -2) and (0,-3). You would start from the y-intercept of the second point, and insert them all into the formula.
AVERAGE RATE OF CHANGE : -0.50
Answer:
Step-by-step explanation:
<u>Key skills needed: Exponent multiplication, Multiplication</u>
1) We have the expression -->
2) We have to simplify this (the parentheses mean multiplication)
The easiest thing to do is: Multiply 4 and 6 --> 4 x 6 = 24.
3) With the step above, the expression now would be .
We now have to do ×
For this we have to use this exponent rule --> ×
=
.
4) This means that ×
=
5) So the simplified expression would be -->
<em>Hope you understood and have a nice day!! :D</em>