– HERE’S AN APPLICATION

PROBLEM INVOLVING REVENUE COSTS

AND PROFIT THAT CAN BE SOLVED

USING A LINEAR EQUATION. A COMPANY MAKES PHONE COVERS. THEY SELL EACH COVER FOR $12. IF X EQUALS THE NUMBER

OF PHONE COVERS PRODUCED AND SOLD, WHAT IS THE REVENUE EQUATION? WELL THE REVENUE WOULD BE

THE TOTAL AMOUNT OF MONEY GENERATED FROM THE SALE

OF THE PHONE COVERS SO WE CAN SAY

THAT THE REVENUE BIG R, IS GOING TO BE EQUAL TO 12 x X WHERE AGAIN X IS THE NUMBER

OF PHONE COVERS PRODUCED AND SOLD. AND R WOULD BE

THE TOTAL REVENUE IN DOLLARS. NEXT THE COST TO MAKE

THE COVERS IS $2 EACH WITH A ONE TIME START UP COST

OF $5,200. SO NOW WE WANT TO KNOW

WHAT THE COST EQUATION IS. AND WE CAN SEE THERE ARE

TWO COMPONENTS TO THE COST, THERE’S THIS FIXED COST

OF $5,200 THAT’S NOT GOING TO CHANGE AND THEN WE HAVE

A VARIABLE COST BASED UPON THE NUMBER OF PHONE

COVERS PRODUCED AT $2 EACH. SO THE TOTAL COST IS GOING TO BE EQUAL TO 2 x THE NUMBER

OF PHONE COVERS PRODUCED, PLUS THE FIXED COSTS,

OR START UP COSTS OF $5,200. SO C IS GOING TO REPRESENT

THE TOTAL COST IN DOLLARS WHERE X IS THE NUMBER

OF PHONE COVERS PRODUCED. AND IT’S PRETTY TYPICAL

TO LEAVE THE UNITS OFF IN THE EQUATION AND JUST MAKE A NOTE FOR

WHAT THE VARIABLES REPRESENT. NOW WE WANT TO DETERMINE

THE PROFIT WHEN THE COMPANY SELLS

1,200 COVERS. SO THE FIRST THING

WE SHOULD DO IS WRITE THE PROFIT EQUATION AND PROFIT IS EQUAL

TO REVENUE MINUS COSTS. AGAIN WHERE REVENUE IS

THE AMOUNT OF MONEY COMING IN AND THE TOTAL COST IS

THE AMOUNT OF MONEY GOING OUT. SO THE PROFIT, BIG P, IS GOING TO BE EQUAL

TO THE REVENUE EQUATION OF 12X – THE COST EQUATION

OF 2X + 5,200. NOW IT IS IMPORTANT

THAT WE ADD PARENTHESIS HERE BECAUSE WE DO HAVE TO SUBTRACT

THE ENTIRE COST EQUATION. WE DO HAVE LIKE TERMS HERE

AND HERE SO WE CAN SIMPLIFY

THIS EQUATION. WE’RE GOING TO HAVE

THE PROFIT, IT’S GOING TO BE EQUAL

TO 12X – 2X, THAT WOULD BE 10X AND THEN THIS WOULD BE

MINUS 5,200. SO NOW WE CAN USE

THIS EQUATION TO DETERMINE THE PROFIT WHEN THE COMPANY SELLS

1,200 COVERS. THE PROFIT WOULD BE EQUAL

TO 10 x 1,200 – 5,200. WELL HERE WE’D HAVE

12,000 – 5,200 SO THIS DIFFERENCE WOULD BE

THE COMPANY’S PROFIT FROM SELLING 1,200 COVERS SO THE PROFIT IS GOING TO BE

EQUAL TO– THIS WOULD BE $6,800. AND THE LAST QUESTION ASKS US

TO FIND THE NUMBER OF COVERS THEY NEED TO SELL

TO BREAK EVEN. WELL BREAK EVEN IS WHEN THE

COMPANY DOESN’T MAKE ANY MONEY OR LOSE ANY MONEY. SO THAT WOULD OCCUR WHEN THE REVENUE

IS EXACTLY EQUAL TO THE COST. SO TO DETERMINE

THE BREAK EVEN POINT WE’LL HAVE TO SET THE REVENUE

EQUAL TO THE COST WHICH MEANS WE’LL HAVE

12X=TO 2X + 5,200. SO TO SOLVE FOR X HERE, WE’LL

SUBTRACT 2X ON BOTH SIDES. WE WOULD HAVE 10X=5,200. LET’S GO AHEAD

AND FINISH THIS UP HERE. SO WE’LL DIVIDE BOTH SIDES

BY 10, SO WE HAVE X=5,200 DIVIDED

BY 10 WHICH WOULD BE 520. SO THEY NEED TO SELL 520

COVERS TO BREAK EVEN, MEANING THEY WON’T MAKE

ANY MONEY OR LOSE ANY MONEY. I HOPE YOU FOUND THIS HELPFUL.

thanks for the easy example…really breaks it down to fully understand.