The owner of Chips etc. produces two kinds of chips: lime (L) and vinegar (V) . He has a limited amount of the three ingredients used to produce these chips available for his next production run: 4800 ounces of salt, 9600 ounces of flour, and 2000 ounces of herbs. A bag of lime chips requires 2 ounces of salt, 6 ounces of flour, and 1 ounce of herbs to produce; while a bag of vinegar chips requires 3 ounces of salt, 8 ounces of flour, and 2 ounces of herbs. Profits for a bag of lime chips are $0.40, and for a bag of vinegar chips $0.50.
-Which of the following is not a feasible production combination?

Question

Quizplus · Accepted Answer

To determine the feasible production combinations, we can use the constraints given by the available ingredients:

2L + 3V ≤ 4800 (salt constraint)
6L + 8V ≤ 9600 (flour constraint)
1L + 2V ≤ 2000 (herbs constraint)

We also know that the production levels must be non-negative (we can't produce a negative amount of chips), so L and V must be greater than or equal to zero.

Using these constraints, we can check each of the given options:

A) 0L and 0V: This option satisfies all the constraints, since we are not producing any chips. This is a feasible production combination.

B) 0L and 1000V: Using the constraints, we can check if this option is feasible:

2(0) + 3(1000) = 3000 (salt constraint)
6(0) + 8(1000) = 8000 (flour constraint)
1(0) + 2(1000) = 2000 (herbs constraint)

This option also satisfies all the constraints, so it is feasible.

C) 1000L and 0V: Again, using the constraints, we can check if this option is feasible:

2(1000) + 3(0) = 2000 (salt constraint)
6(1000) + 8(0) = 6000 (flour constraint)
1(1000) + 2(0) = 1000 (herbs constraint)

This option also satisfies all the constraints, so it is feasible.

D) 0L and 1200V: Let's check if this option is feasible:

2(0) + 3(1200) = 3600 (salt constraint)
6(0) + 8(1200) = 9600 (flour constraint)
1(0) + 2(1200) = 2400 (herbs constraint)

This option violates the salt constraint, since we only have 4800 ounces of salt available and this option requires 3600 + 0 + 0 = 3600 ounces. Therefore, this option is not feasible.

The best choice(s) depend on the objective (maximizing profit, minimizing cost, etc.). However, one possible optimal combination can be obtained by calculating the profit for each feasible combination and choosing the one with the highest profit. We can use the profit function:

Profit = 0.4L + 0.5V

And the feasible combinations (found above) to calculate the profit for each option:

A) 0L and 0V: Profit = 0
B) 0L and 1000V: Profit = 0.5(1000) = 500
C) 1000L and 0V: Profit = 0.4(1000) = 400
D) 0L and 1200V: Not feasible

Therefore, the best choice(s) are options B and C, since they have the highest profit. Depending on the specific objective and constraints, there could be other optimal combinations.

The Owner of Chips Etc