A company produces two different products. They require two types of ingredients: M and N. The first product require 90 grams of the ingredient M and 10 grams of the ingredient N. The second product require 20 grams of both ingredients. The company has a maximum of 2,100 grams of the ingredient M and because of a contract with suppliers has to maintain in stock 500 grams of the ingredient N. Also, the company has agreed with a buyer to produce at least 10 items of the first product. The cost of production of the first product is 10 dollars and 20 dollars for the second. There is a fixed cost of production of $100.
- How many units of both products should be produced so the company minimizes its cost?
- What is the minimum cost?
Ok, this is what I have done. I've identified the decision variables as
- x: the first product
- y: the second product
The objective function es $$C = 10x+20y+100$$
$$x\geq0$$ $$y\geq0$$ $$90x+20y\leq2100$$ $$10x+20y\geq500$$ $$x\geq10$$
When I do the graph I get these vertexes (see the graph below) of the feasible region but the problem is that when I evaluate them in the objective function I get "two optimal solutions" when I think should be one. These are the results when I evaluate the objective function with the vertex:
- (10,60) -> 1400
- (10,20) -> 600
- (20,15) -> 600
Could someone help me!!! So is everything right with the whole process? or do I have something wrong that I'm getting two optimal solutions? I need some lighting.
This is the graph: