When a vendor prices key chains at 5 each she sells 210 key

When a vendor prices key chains at $5 each, she sells 210 key chains. For each $1 she raises the price, she sells 10 fewer key chains. USE AN EQUATION to determine what she should charge to maximize her revenue from sales.

Solution

when price is $ 5 each , she sells 210 key chains

when price is $ 6 each , she sells 200 key chains

(p₁,x₁)=(5,210),(p₂,x₂)=(6,200)

x-x₁=[(x₂-x₁)/(p₂-p₁)](p-p₁)

x-210=[(200-210)_/(6-5)](p-5)

x-210=-10(p-5)

x-210 =-10p+50

x=-10p +260

revenue R=xp

R=(-10p +260)p

R=-10(p² -26p)

R=-10(p² -26p+(26_/2)²-(26_/2)²)

R=-10(p² -26p+13²-13²)

R=-10(p² -26p+13²)+1690

R=-10(p -13)² +1690

function is parabola which is open downwards , vertex is (13,1690)

she should charge 13 dollars each to maximise her revenue. maximum revenue is 1690 dollars