An engineer orders 8,000 liters of solvent for a pollution control equipment at P1.50 per liter and for every one centavo subtracted from the cost per liter,500 more liters will be ordered,at what price per liter will the solvent dealer charge to give a maximum sale?

a. 45 cents

b. 83 cents

c. 72 cents

d. 67 cents

Question

An engineer orders 8,000 liters of solvent for a pollution control equipment at P1.50 per liter and for every one centavo subtracted from the cost per liter,500 more liters will be ordered,at what  price per liter will the solvent dealer charge to give a maximum sale?

a. 45 cents 

b. 83 cents

c. 72 cents

d. 67 cents

anonymous · Answer

we can write this as sales = (1.50 - x)(8000 + 500x) where x represents decrease by one centavo

anonymous · Answer

$$(1.50-x)(8000+500x)=-500 x^2-7250x+12000$$ a parabola that opens down. your job is to find the vertex

anonymous · Answer

you good from there?

anonymous · Answer

im a filipino i dont know cents...

anonymous · Answer

w8 i try

anonymous · Answer

the units are unimportant. call them centavos is fine

anonymous · Answer

44.5 or 45 cents? when u say x represents decrease by 1 centavo

phi · Answer

We have to tweak sat's equation.  A quick google search shows there are 100 centavos in a peso.  So the equation should be
$(150-x)(8000+500x)= $price (centavos)

This is the same as
$$ -500x^2 +75000x-8000x+1200000= -500x^2 +67000x+1200000$$

Now find the peak of the parabola using -b/2a  where b= 67000 and a= -500
$$ \frac{-67000}{2\cdot -500} = 67 \text{ centavos }$$

67 is the discount.  To answer "at what  price per liter will the solvent dealer charge "
we deduct 0.67 pesos from 1.50 pesos to get 0.83 pesos, or 83 centavos

anonymous · Answer

thanks, i didn't catch that.  i made the erroneous assumption that "cent' was short for "centavo"

phi · Answer

I only noticed when I kept getting a negative x.  Something is fishy here....