Scenario 15.1 - The Jerk Store
George takes an eclectic mix of spices to make his authentic jerk seasoning as a rub for chicken, pork, and fish. The ingredients and packaging cost $1.50 and he sells the packets by the case to Jerk Stores in the Caribbean for $2.50 per packet. Tourists to the islands gladly pay $8.75 for these packets, eager to host their friends for an authentic Caribbean meal and bore them with vacation photos upon their return. The demand for the packets is normally distributed, with a mean of 2500 packets and a standard deviation of 600.
-If each Jerk Store location is acting independently, what is their expected profit if they stock an optimal quantity?

Question

Quizplus · Accepted Answer

To find the optimal quantity that maximizes profit, we need to use the formula for expected profit:

Expected Profit = (Demand x Selling Price) - (Quantity x Cost)

We can find the optimal quantity by taking the derivative of this formula with respect to quantity and setting it equal to zero. This gives us:

Selling Price - Cost = (Demand / Quantity)

Solving for Quantity, we get:

Quantity = sqrt(Demand x (Selling Price - Cost))

Plugging in the given values, we get:

Quantity = sqrt(2500 x (8.75 - 2.5)) = 149.13

Since we can't stock a fractional number of packets, we should round up to 150 packets.

Plugging this quantity into the expected profit formula, we get:

Expected Profit = (2500 x 8.75) - (150 x 1.5) = $13,840

Therefore, the best choice is B, with an expected profit of $13,840.

Scenario 15.1 - the Jerk Store