SOLUTION: The following information relate to Kathurima Ltd, a dealer in standard wooden furniture on the outskirts of the city of Nairobi. The company realized profits of Sh. 120,000 from

Question 1135748: The following information relate to Kathurima Ltd, a dealer in standard wooden furniture on the outskirts of the city of Nairobi. The company realized profits of Sh. 120,000 from 7 tables, Sh. 124,000 from 9 tables and Sh. 113,000 from 4 tables made and sold. Kathurima has now approached you for assistance in forecasting future profits. The profit function is believed to be quadratic in nature. What will be Kathurima Ltd’s profit function to be used in forecasting?
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
The ordered pairs (using thousands of Sh.) are (4, 113) (7, 120) and (9, 124)
put these into ax^2+bx+c=y
so 16a+4b+c=113
49a+7b+c=120 and
81a+9b+c=124
The first and second give
-112a-28b-7c=-791
196a+28b+4c=480
84a-3c=-311
first and third give
-144a-36b-9c=-1017
324a+36b+4c=496
180a-5c=-521
those two become
420a-15c=-1555
-540a+15c=1563
-120a=8
a=-(1/15) or -0.0667
therefore 4b+c=113+16/15=114.0667 (114.1)
and (third) 9b+c=131.4
-5b=-17.3
b=3.46
c=100.26
the equation is -0.0667x^2+3.46x+100.26=f(x)
in THOUSANDS of Sh.
RELATED QUESTIONS
The longest drive to the center of a square city from the outskirts is 10 miles. Within... (answered by lwsshak3)

The boundary of a city is a circle of diameter d = 6 miles. As shown in the figure, a... (answered by chessace)

The outdoor furniture center buys wooden benches for $50 each. The furniture store owner (answered by addingup)

A cabinetmaker completes the initial work on a piece of furniture in 9 hours. This work... (answered by josmiceli)

A furniture store has a sale offering 10% off of all furniture. If Amanda... (answered by ewatrrr)

Translate the English sentence into an equation using the variables indicated: The ratio... (answered by fractalier)

Translate the English sentence into an equation using the variables indicated: The ratio (answered by checkley71)

The Chief Economist of Analytics Financial Investments Services (AFIS) Pty Ltd, Prof.... (answered by Boreal)

Classic Furniture Concepts has determined that when x hundred wooden chairs are built,... (answered by MissMath314)