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Situation: A sandwich shop sells its signature sandwich for $4.75 and at this price, sells 500 sandwiches per

month. A survey indicates that an additional 125 people would buy this sandwich each month for every $0.25

decrease in the price.

a) Determine the demand (or price) function. Show your steps and define your variables.

b) Determine the revenue function.

c) Determine the revenue when 350 sandwiches are sold.

d) Determine the marginal revenue function

e) Determine the marginal revenue when 350 sandwiches are sold. What does this represent?

f) The cost, C, in dollars of producing x sandwiches is C = 0.007x


2 − 20x + 2500. What is the cost of making 350 sandwiches?

g) What is the marginal cost of making 350 sandwiches? What does this represent?

h) Determine the actual cost for making the 351th sandwich.

i) Determine the profit function in simplest form.

j) Determine the profit of selling 350 sandwiches. What does this represent?

k) Determine the marginal profit of selling 350 sandwiches. What does this represent?

l) Determine the actual increase in profit that the company will receive by selling the 351th sandwich.

m) How many sandwiches must be sold to reach the maximum profit? Solve using method in the derivatives

unit. Hint: use a sin chart. Round to the nearest whole number.

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