The Booster Shot Hot Sauce Company uses dried peppers to make their product. Specifically, they use three types of peppers: Chipotle peppers, New Mexico peppers, and Serano peppers. The other ingredients are minimal and can be ignored. They wish to mix up a batch that is exactly 100 kg.

In order to get the right mix they look at three characteristics: Capsaicin — the component that contributes spiciness — must be at least 500 grams out of the 100 kg total. Smokiness must be at least 1500 g out of the 100 kg total. Colour must be between 7000 and 8000 points, out of the 100 kg total batch. The contributions, per kg, from each pepper type are as follows:

	per kg
	Chipotle	New Mexico	Serano
capsaicin (grams)	2 2/3	4	18
smokiness (grams)	50	3	2
colour (points)	60	95	5

The cost per kg for the peppers is $11.75 for Chipotle, $7.50 for New Mexico, and $9.55 for Serano.

The recipe calls for at least 30 kg of Chipotle and at most 25 kg of Serano, in a 100 kg batch.

Construct an LP to find the lowest cost recipe. Then answer the following questions:

How many constraints are there for colour?

• # of colour constraints:

How many nonnegativity constraints are there?

• # nonnegativity constraints:

How many constraints are there in total?

• # constraints:

How many kg of Chipotle peppers are used in the optimal solution?

How many kg of New Mexico peppers are used in the optimal solution?

And how many kg of Serano peppers are used at the optimal solution?