grocery asked in Science & MathematicsMathematics · 3 months ago

# Solving Quadratic Inequalities in One Variable?

800 people will attend a concert if tickets cost \$20 each. Attendance will decrease by 30 people for each \$1 increase in the price. The concert promoters need to make a minimum of \$12 800.

What quadratic inequality represents this situation?

What is the range of ticket prices the concert promoters can charge and still make at least the minimum amount of money desired?

Relevance
• Anonymous
3 months ago

Source(s): Womenwearheadscarvestiedatthefronttopreventheadachesfromskypushingdownandtopreventthroatcancer. Megatsunami forNewYork willbe400 meters;then engulfed-in-lava LosAngeles willbe floodedtoo; also, asteroid destroys Gulf of Mexico; onlyAlaska (soonwilljoinRussia), Eurasia, and Africa remain (obviously without coasts). 1stbigearthquake in Russia; 2nd bigger one in China (willbesplitinhalf;peoplewillfallinto this hole;radiation!); 3rdbiggestwillbeintheUSA (GreekOrthodoxmonkElidiyfromAfrica). Mutantsfromgov’tlabswillescapeaftertheearthquake; youneed guns/ammo todealwiththem; if gov’ttries totakeyourgunsaway, givethemonewhile leavingthreehidden (to deal with mutants). If gov’twilltakeyoutoaconcentrationcamp, have a bag of old very worn warm clothes (so that they won’t be stolen when you’retakingashower)and specialcuptomeltsnow. If the last descendant rejects mark of the beast, then his/her ancestors go to heaven (saint Vyacheslav Krasheninnikov = Archangel Uriel); forgive me
• 3 months ago

For an increase of p dollars above \$20, the attendees will decrease by 30

so, -30(p - 20)

As there are 800 attendees when the price is \$20 we have.

A = 800 - 30(p - 20) => 1400 - 30p

If each attendee pays p, then the overall income will be:

Ap = p(1400 - 30p) = 1400p - 30p²

This value needs to be 'at least' \$12800

i.e. 1400p - 30p² ≥ 12800

or, 3p² - 140p + 1280 ≤ 0

Critical values are when 3p² - 140p + 1280 = 0, so using the quadratic formula we get:

p = (140 ± √4240)/6

so, p = 12.48 or 34.19

Hence, 12.48 ≤ p ≤ 34.19

Note: As the quadratic is symmetrical about these values the maximum value will occur when p is the mean

i.e. p = (12.48 + 34.19)/2 => 23.33

:)>

• Sean
Lv 5
3 months ago

yield function p = price

p*(800- 30*(p-20)) which is 16000\$ as required for 800 tickets

1400*p -30*p^2

equate to 12800\$

-30*p^2 + 1400*p + 600  = 12800\$

-30*p^2 + 1400*p -12800 = 0

divide by 100

-.3*p^2 +14*p -128 = 0

solve by formula

(-14 +/- sqrt(196 - 153.6)/-.6

(-14 +/-  6.5)/-.6

-7.5/.-.6 , 20.5/.6

12.5, 34.2 is the acceptable range

(24.35 the halfway point between will as usual be the optimum value)

• 3 months ago

A = attendance

P =  price

A = 800 -30 (p-20)

Income = A * P = 800p - 30p ( p-20)

= 800p - 30p^2 +600p

= -30p^2 + 1400p

Set that equal to 12800, and solve for p.

p = 12.47 to 34.18 or in round dollars, p = 13 to 34.