A coffee company sells two types of breakfast blends. They have on hand 132 kg of dark roast and 84 kg of hazelnut. One breakfast blend will contain half dark roast and half hazelnut and will sell for $ 7 per kg. The other breakfast blend will contain 3/4 dark roast and 1/4 hazelnut and will sell for $ 9.50 per kg.My approach:I see this is an optimization problem and need to show that 132 x 1 + 84 x 2 needs to be optimized but confused on the other constraintsI used the convex optimization polygon theory of checking on the endpoints and computing the maximal value, can someone check and elaborate further on the reply below?

Question

A coffee company sells two types of breakfast blends. They have on hand 132 kg of dark roast and 84 kg of hazelnut. One breakfast blend will contain half dark roast and half hazelnut and will sell for   $  7 per kg. The other breakfast blend will contain 3/4 dark roast and 1/4 hazelnut and will sell for   $  9.50 per kg.My approach:I see this is an optimization problem and need to show that   132      x    1    +  84      x    2   needs to be optimized but confused on the other constraintsI used the convex optimization polygon theory of checking on the endpoints and computing the maximal value, can someone check and elaborate further on the reply below?

Elijah Benjamin · Accepted Answer

Let       x    1   denote the number of &quot;blend 1&quot; breakfasts and       x    2   the number of &quot;blend 2&quot; breakfasts that the company will sell. Then you want to maximize the profit of the company, which is  max  7      x    1    +  9.5      x    2  subject to (the capacity constraints)      1    2        x    1    +      3    4        x    2    ≤  132        1    2        x    1    +      1    4        x    2    ≤  84where   0  ≤      x    1    ,      x    2  .

A coffee company sells two types of breakfast blends. They have on hand 132 kg of dark roast and 84

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