Download 5. Pizza Problem

5. Pizza Problem
WK#9 (p. 4 of 4)
(Complete this yourself first. Follow the procedure used in the Football Problem. Then compare your answers
with Example 1 on p.205 in textbook. Correct your work, if necessary. Continue reading example 2 on p.207)
An old Pizza Inn menu from the 1960’s lists the following prices for plain cheese pizzas:
Small (8”diameter)……… 85 cents
Medium(10”diameter)…….. 115 cents
Large (13” diameter)……… 175 cents
a. Assume that the price is a function of the diameter. Is it possible for this to be a linear
function? Defend your answer.
b. Let’s assume the price is a quadratic function of the diameter.
(Is this a fair assumption? Remember the formula for the area of a circle.)
Write the particular equation expressing price in terms of diameter.
(Remember: Write 3 ordered pairs and use Matrices)
Let d = number of inches of the pizza’s diameter
Let p = number of cents for a pizza
c. Suppose that the menu had listed a “Colossal” pizza costing $6.00 (600 cents).
What do you predict its diameter would have been?
d. The price-intercept is the price when the diameter is zero. (When there is no pizza!) What
does the price-intercept equal in this math model? Why is it greater than zero?
e. Use the discriminant to show that there are no diameters for which the price is zero.
f. Using this mathematical model, determine Pizza Inn’s minimum cost pizza and the size of that
pizza. Explain why this model may not be appropriate for very low prices/sizes.
g. Using the information determined above, sketch a graph of this function in a reasonable
domain.
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