Question

QUESTION 3 Oily oil company has decided to introduce three oil mixes made from blending two or more 15 Marks] oils. One jar of olive-vegetable oil requires 6 oz each of olive and vegetable oils. One jar of vegetable peanut oil requires 10 oz of vegetable oil and 6 oz of peanut oil. Finally, one jar of olive-vegetable-peanut oil requires 3 oz of olive oil, 7 oz of vegetable oil, and 2 oz of peanut oil. The company has decided to allot 15,000 oz of olive oil, 23,000 oz of vegetable oil, and 4000 oz of peanut oil for the initial production run. Its profit on one jar of olive-vegetable oil is R20.10, its profit on one jar of vegetable-peanut oil is R25.70, and its profit on one jar of olive- vegetable-peanut oil is R25.60. To realize a maximum profit, how many jars of each blend should the company produce? Clearly discuss the following basic optimization formulation steps relative to the aforementioned problem statement: i. Defining the decision variables Choosing an objective function Identifying the constraints

Optimization Problem

Answer 1

Let

x be the number of jars of olive-vegetable oil

y be the number of jars of vegetable-peanut oil

z be the number of jars of olive-vegetable-peanut oil

So in this problem our decision variables are x , y and z

So the objective function is to maximize the total profit. (where the coefficients represents the profit per bottle oil.)

Thus the objective function is

Maximize T= (20.10)x + (25.70)y + (25.60)z  

The constraints are:

6x + 3 z ≤ 15000          (for olive oil)

6x + 10y + 7z ≤ 2300      (for vegetable oil)

6y + 2z ≤ 4000                  (for peanut oil)

And x, y, z ≥ 0     (as they represent the number of bottles)

Answer 2