SOLUTION: Units sold (x) and profit(p) are linear. 150 units sold results in $200 profit and 200 units sold results in $3100 profit , write the profit function. P = Find the marginal

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: Units sold (x) and profit(p) are linear. 150 units sold results in $200 profit and 200 units sold results in $3100 profit , write the profit function. P = Find the marginal       Log On


   



Question 998305: Units sold (x) and profit(p) are linear. 150 units sold results in $200 profit and 200 units sold results in $3100 profit , write the profit function.
P =
Find the marginal profit?

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!


P+=ax%2Bb
if 150 units sold results in $200 profit, we have
200+=a%2A150%2Bb
200+=150a%2Bb...solve for b
b=200+-150a....eq.1
if 200 units sold results in $3100 profit, we have
3100+=a%2A200%2Bb
3100+=200a%2Bb...solve for b
b=3100+-200a....eq.2
since left sides of eq.1 and eq.2 are same, equal right sides
200+-150a=3100+-200a...solve for a
200a+-150a=3100+-200
5cross%280%29a=290cross%280%29
5a=290
a=290%2F5
highlight%28a=58%29
now find b
b=200+-150a....eq.1...substitute 58 for a
b=200+-150%2A58
b=200+-8700
highlight%28b=-8500%29
so, your equation is:
highlight%28P+=58x-8500%29