A math problem I need help with

[akaiyou]

So i have the following math problem and im stumped.

A department store's revenue, in millions, can be approximated using the equation R=-0.57y^2+28.88y+115.01, where R represents the revenue each year from 1998 to 2004 and y represents the number of years since 1998, which corresponds to y=0. In what year between 1998 and 2004 did the department store's revenue reach $249 million?

Anyone know the answer? An explanation on how to solve this would also be great.

[swarm492]

This (please do not swear) seems oddly familiar to the stuff from my distribution analysis class. I don't remember how to do it but I might have some work around that might have some steps on it. I take a look.

[akaiyou]

Sounds good

[swarm492]

I cant get the entire assignment to post, but does this look familiar? It uses the E.P.L.S model. I was also wrong on the class, its for quantitative analysis of business.

B. To determine the lot size that would minimize our total annual cost we will use the E.P.L.S model, and by analyzing the given scenario we can plug in the required information to utilize this model.


D-demand per year-15,000 units
d-demand per day-41 units
P-production of units per year-60,000 units
p-production per day-164 units
Co-setup costs per run-$84
Ch-holding cost per unit per year is 28% or $5.32 cents per unit per year

Because we are only interested in the optimal lot size needed by Company B to achieve their minimal total annual cost (Q*) we can use the equation.


Q*=794.7194142
Q*=795

By using the this formula from the E.P.L.S model we can determine that the optimal lot size for Company B is 795.

[akaiyou]

So do you have an answer to the problem I posted? Seems like your problem might correlate with this one but not entirely, so it just serves to confuse me further.

[acmemyst]

Sure.

Regression formula:
R=-0.57y^2+28.88y+115.01

Equate to target value:
-0.57y^2 + 28.88y + 115.01 = 249

Rearrange:
-0.57y^2 + 28.88y - 133,99 = 0

Find y using quadratic formula ( en.wikipedia.org/wiki/Quadratic_equation ):
y = (-28.88 +- sqrt(28.88^2 - 4*-0.57*-133.99)) / (2*-0.57)

y = 5,1667
OR
y = 45,5

Given the assignment, the correct answer is the year 2003.

Also,



Cheers

[akaiyou]

Thank you very much that actually made a lot of sense the way you solved it. Appreciate it

[yoritomo]

It's just a quadratic equation. All you need to do is set R to 249 and solve for y. You can factor by hand or use the quadratic formula.

Anything in the form 0=ax^2+bx+c can easily be solved by the quadratic formula.