A pharmaceutical company decided to manufacture new food supplement pills. It will need to add some vitamins to the mix. It decides on two vitamin mixes: Vitamin mix 1 and Vitamin mix 2. Vitamin mix 1 costs $40 and will contain 2 units of vitamin B and 5 units of vitamin C. Vitamin mix 2 costs 35 USD and will contain 2 units of vitamin B and 3 units of vitamin C. For nutritional reasons, both mixes have to contain at least 12 units of vitamin B and 15 of vitamin C. Formulate a linear programing model based on the given data.

Minimize: Cost = 40X+35Y

Subject to: 2X + 2Y ≥ 12

5X + 3Y ≥ 15

Step-by-step explanation:

To formulate a linear programming model we need to identify the variables of decision, the objective functions and the constraints.

So, the variables of decision are the quantity of every vitamin mix and we are going to call:

X: The quantity of vitamin mix 1

Y: The quantity of vitamin mix 2

Our objective function is going to be minimize the cost of the both mixes, so, the objective function is:

Minimize Cost = 40X + 35Y

Because vitamin mix 1 cost $40 and vitamin mix 2 cost $35

Finally, the constraints are defined by the following sentence: both mixes have to contain at least 12 units of vitamin B and 15 of vitamin C. Ot means that we have a constraint for vitamin B and a constraint for vitamin C.

Then if Vitamin mix 1 contains 2 units of vitamin B and vitamin mix 2 contain 2 units of vitamin B, the constraint associated to vitamin B is:

2X + 2Y ≥ 12

And, if Vitamin mix 1 contains 5 units of vitamin C and vitamin mix 2 contain 3 units of vitamin C, The constraint associated to vitamin C is:

5X + 3Y ≥ 15

So, the linear programing model is:

Minimize: Cost = 40X+35Y

Subject to: 2X + 2Y ≥ 12

5X + 3Y ≥ 15