Question

A manufacturer is studying the effects of cooking temperature, cooking time, and type of cooking oilfor making potato chips. Three different temperatures,4 different cooking times, and 3 different oils are to be used.
a. What is the total number of combinations to be studied?
b. How many combinations will be used for each type of oil?
c. Discuss why permutations are not an issue in this exercise.

Answer 1

Answer:

(a) The total number of combinations that can be applied for making potato chips is 36.

(b) The number of combinations that will be used for each type of oil is 12.

(c) Permutations are not an issue because order does not matter.

Step-by-step explanation:

The effects of cooking temperature, cooking time and cooking oil is studied for making potato chips.

The number of different temperatures applied is, n (T) = 3.

The number of different times taken is, n (t) = 4.

The number of different oils used is, n (O) = 3.

If an assignment can be done in n₁ ways and if for this assignment another assignment can be done in n₂ ways then these two assignments can be performed in (n₁ × n₂) ways.

(a)

Compute the total number of combinations that can be applied for making potato chips as follows:

Total number of combinations for making chips = n (T) × n (t) × n (O)

                                                                               $=3\times4\times 3\\=36$

Thus, the total number of combinations that can be applied for making potato chips is 36.

(b)

To make potato chips 4 different temperatures are used and 3 different oils are used.

Each of the oil type is cooked in 4 different temperatures.

So the number of ways to select each oil type is,

n (T) × n (O) = $4\times3=12$

Thus, the number of combinations that will be used for each type of oil is 12.

(c)

Permutation is the arrangement of objects in a specified order.

Since in this case ordering of the the three effects, i.e. temperature. time and oil type is not important, permutations are not an issue.