me fast, you so much d e f Transcribed Image Text: Tom and Jerry are opening a food truck named the T & J Box in New York

me fast, you so much d e f Transcribed Image Text: Tom and Jerry are opening a food truck named the T & J Box in New York.
(a)
Suppose f(p) is the number of sandwiches they sell at price p. From the short
experience of working a food truck, Tom estimates that if the price of each sandwich is $7 then
they will sell 800 sandwiches and Jerry estimates that f'(7) = –50. Explain in your own
words what f’ (7) = -50 means in practical terms.
(b)
Suppose R(p) is the revenue (i.e. total sales in dollars) obtained when selling
sandwiches at price p. What is the revenue when the price is $7 per sandwich? In other words,
find R(7).
(c)
Calculate R’ (7) and explain in your own words what it means in practical terms.
(d)
Define the cost function g(n) = cost of making n sandwiches. Assume the cost to
make 800 sandwiches is $2000, and g'(800) = 1.50. Explain in your own words what
g’ (800) = 1.50 means in practical terms.
(e)
The number n of sandwiches they sell at price p is given by f(p), thus the cost
function C(p) as a function of the price p is given by
C(p) = g(f(p)). Can you use the chain rule to evaluate C’ (7)?
(f)
Tom and Jerry want to increase their profit. Should they increase the price from $7
to $8 per sandwich? Why or why not? Use the profit formula
P = R – C (profit equals revenue minus cost), calculate P’ (7), and argue from here.

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