Write an expression in terms of x for the following: a. the cost of the tie after its price is reduced by $x.?

Question

The Sell-Rite Corporation sells men's ties.The ties are priced at $26 each and they have been selling an average of111 per week.A consultant has determined that for each dollar the company reduces the price of ties, an additional13 ties would be sold.1.Write an expression in terms of x for the following:a.he cost of ties afster its price is reduced by $x.b.the # of ties sold per week after the price id reduced by $x. c.he sales revenue per week after reducing the price by $x.2.What price reduction, to the nearest cent, will maximize the sales revenue on ties?3.At this price reduction, find the new selling price and the average number of ties Sell-Rite can expect to sell per week.4.Sell-Rite spends$11.50to purchase each tie. They will consider only price changes that result in net profit (they will not sell ties for less than it costs to make them).Under these conditions,find the domain and range of the revenue function.How would this change if Sell-Rite could produce the ties for $9.75

Answer 1

1.
a) price of ties after being reduced by x: 26-x
b) # of ties sold per week after price reduction of x: 111 + 13x
c) sales revenue per week after price reduction of x:
(26-X)(111 + 13X ) = R
2.
dR/dx = 0 yields x(max) = $8.73 to maximize sales revenue.
3.
New selling price = 26-8.73 = 17.27
Avg number of ties per week at this price = 111 + 13(8.73)= 111 + 113.49 = 224.49. ( Even 'tho' you can't sell half a tie, the average number sold would be 224.49 )
4.
(26-x )> 11.50 ( domain x=0, 14.5 ); this corresponds to endpoints ( R=111(26), 3445.25 ) or (R = 2886, 3445.25 ). However, R has a maximum for x=8.73 where R = 3876.94 so the range is R = 2886, 3876.94
If the cost were 9.75, the domain would be (26-x)>9.75 or
(x = 0, 16.25 ) and the endpoints ( R = 2318.06, 3445.25 ) but R would still have a maximum at x = 8.73 so the range of R is R = 2318.06, 3876.94.

Answer 2

x² - 2x – 3 -------------- 2x² - 8x + 6 (x – 3) (x + a million) => ---------------- (x – 3) (2x – 2) you are able to now cancel (x – 3) from the numerator and the denominator so we’r left with (x + a million) -------- 2(x – a million) it quite is the answer. The confusing section the following is splitting (x² - 2x – 3) into (x – 3) (x + a million) and likewise contained in the denominator. Its easily factorizing a quadratic equation. I actual have extra a link which elaborates somewhat yet on factorizing, yet there are a kind of different the top thanks to do it