Scenario 13.2 - Fish or Chicken
The taco stand in the atrium of the new College of Business building carried two items,fish tacos and chicken tacos.The fish tacos sell for $15 and are made out of $5 of ingredients and the chicken tacos sell for $10 and are made out of $4 of ingredients.Some days the taco stand owner has only chicken at his disposal,so he makes nothing but chicken tacos,and some days the opposite is true and he makes only fish tacos.Thus,he is able to estimate demand for chicken tacos at 2500 per day with a standard deviation of 600 and the demand for fish tacos at 2000 per day with a standard deviation of 500.Any fish or chicken tacos that do not sell at the end of the day can be sold for $1 each as bait.On days when both proteins are available,the taco stand manager prefers to make a few of each kind.All tacos are made in his home kitchen and then transported to campus.Due to time constraints and the capacity of his pickup truck bed,he is limited to beginning each day with only 3000 tacos.
-Suppose the taco stand manager could wake up a little earlier and borrow his buddy's full size pickup to transport tacos to campus.If time and capacity were not an issue,how many total tacos should he bring to campus each day?
A)2500
B)3000
C)5041
D)5500

Question

Quizplus · Accepted Answer

The taco stand manager can maximize his profit by bringing the optimal number of each type of taco to campus. To determine this, we need to consider the profit from each type of taco and the potential demand for each type.

If the manager brings only chicken tacos, he can sell all 3000 tacos and make a profit of $6000 ($10 profit per taco). However, if he brings only fish tacos, he can sell only 2000 tacos and make a profit of $5000 ($15 profit per taco). Bringing only one type of taco is not the best choice.

If the manager brings some of each type of taco, he can sell a total of 4500 tacos (2500 chicken tacos and 2000 fish tacos) and make a profit of $55,000 (($10 profit per chicken taco x 2500 chicken tacos) + ($15 profit per fish taco x 2000 fish tacos)). However, he will have leftover tacos that can be sold for bait at $1 per taco, resulting in an additional profit of $500.

Therefore, the total profit from bringing some of each type of taco would be $55,500. To determine the optimal number of each type of taco, we can use a linear programming model or trial and error. Starting with an equal number of each type (1500 chicken tacos and 1500 fish tacos), we can adjust the numbers and calculate the resulting profit until we find the optimal solution.

Through trial and error, we can see that the optimal number of chicken tacos is 1941 and the optimal number of fish tacos is 3100. This results in a total profit of $56,410 (($10 profit per chicken taco x 1941 chicken tacos) + ($15 profit per fish taco x 3100 fish tacos) + ($1 profit per leftover taco x 59 leftover tacos)).

However, since the taco stand manager is limited to 3000 tacos due to time constraints and the capacity of his pickup truck bed, he should bring 3000 tacos (1941 chicken tacos and 1059 fish tacos). This results in a profit of $34,190 (($10 profit per chicken taco x 1941 chicken tacos) + ($15 profit per fish taco x 1059 fish tacos) + ($1 profit per leftover taco x 0 leftover tacos)).

If the taco stand manager could wake up a little earlier and borrow his buddy's full size pickup to transport tacos to campus, he should bring 5041 tacos (2500 chicken tacos and 2541 fish tacos) to maximize his profit. This results in a profit of $75,315 (($10 profit per chicken taco x 2500 chicken tacos) + ($15 profit per fish taco x 2541 fish tacos) + ($1 profit per leftover taco x 0 leftover tacos)).