Question

Suppose that the manager of the pizza restaurant changes his pricing strategy. Instead of charging solely based upon ingredients, he sells each pizza at $8.00 over the cost of the ingredients, no matter what the size. A 12 in. pizza with one topping still costs $12.99. Using his new pricing plan, how much should he charge for a 14 in. pizza with one topping?

Answer 1

zoe11: You need to supply more information for us to be able to help you here.

Answer 2

what was his original pricing strategy?

Answer 3

$8 as cost doen't depend on size and ingridients

Answer 4

oh.. sorry it says
Suppose a restaurant sells 12 inch diameter pizzas with cheese and one topping for $12.99 plus tax. Also suppose that the restaurant bases its prices on the amount of ingredients used to make the pizza, and that the pizzas have the same thickness. What should the restaurant charge for a 14 diameter pizza with cheese and one topping?

Because the tops of both pizzas are circles, they are similar with k = 14/12 = 7/6. An immediate response is to charge 7/6 * 12.99 = 15.16. however, that is not correct becuase the crus and toppings are proportional to the area , not the linear dimensions. so you must multiply by (7/6)^2 not 7/6. (7/6)^2 = 49/36 + 17.68.
usually prices of pizzas are not based only on ingredients. other factors, such as salaries, equipment, and overhead must be taken into account.

Answer 5

thats the example from my book..

Answer 6

ok, so the 12 inch pizza plus one topping must now cost $8 + cost of ingredients. If this still comes to $12.99, then the cost of the ingredients with one topping must be $4.99.
Hence, the cost of a 14 inch pizza with one topping in the new system must also be $12.99 ($8 fixed charge + cost of ingredients for a single topping)

Answer 7

does that make sense?

Answer 8

I'm sort of confused.. are you going off the new or old problem?

Answer 9

new problem states the cost of pizza is now $8 "over the cost of ingredients" - irrespective of size.
this means a pizza in the new system costs $8 plus the cost of all its ingredients.

Answer 10

actually my answer may be wrong here.
for a 12 inch pizza with a single topping, we worked out that its ingredients must have cost $4.99.
so for a 14 inch pizza the ingredients cost need to be multiplied by a factor that takes into account the increased area of the pizza.

Answer 11

so ingredients cost for 14 inch pizza woud be:
(7/6)^2 * $4.99 = (49/36) * $4.99 = $6.79

so 14 inch pizza should cost $8 + $6.79 = $14.79

Answer 12

hope it makes sense now

Answer 13

wait how did you get the $4.99 again?

Answer 14

ok, let me explain in steps...

Answer 15

1. in the new system, the cost of a pizza is $8 plus the cost of all its ingredients.
agreed?

Answer 16

yes

Answer 17

2. in the new system, a 12 inch pizza with one topping costs $12.99. This means that its ingredients cost must be $12.99 - $8 = $4.99

agreed?

Answer 18

I understand the 12 inch pizza costs 12.99, but what do you do with the $8 to get $4.99?

Answer 19

in the new system ALL pizza's cost $8 plus cost of ingredients.
therefore, if a 12 inch pizza with one topping costs $12.99, then it must be made up of:

$12.99 = $8 + (cost of ingredients)

therefore:

(cost of ingredients) = $12.99 - $8 = $4.99

Answer 20

ok! got it so far..

Answer 21

ok, so now for a 14 inch pizza with one topping, its must cost:

$8 + (cost of ingredients for one topping on a 14 inch pizza)

and we know:

(cost of ingredients for one topping on a 12 inch pizza) = $4.99

therefore:

(cost of ingredients for one topping on a 14 inch pizza) = (14/12)^2 * $4.99 = $6.79

therefore 14 inch pizza with one topping should cost:

$8 + $6.79 = $14.79

Answer 22

Why did you square the (14/12)

Answer 23

because the extra ingredients required will depend on the AREA of the pizza - just like i the previous problem

Answer 24

Ah ok I understand now!! thank you so much for taking time to explain it to me!

Answer 25

yw - I'm glad I was able to help.