DJ Mustard has a side business making hot sauces. He is planning production for the coming weeks, and has access to the following hot peppers:

Cost/kg	Supply Limit (kg)	Scoville "Score" (in '000s)
Jalapeno	$10.00	10	2
Serrano	$15.00	10	25
Habanero	$30.00	10	350

He will mix, cook and bottle the peppers with other spices to make three types of sauces. The most important factor is the Weighted Average Scoville Score (WASS), calculated by finding the weighted average of the Scoville scores of the peppers used. For example, a sauce made with 3/4 Serrano and 1/4 Jalapeno by weight has a WASS of ( 25*3 + 2*1 ) / 4 = 19.25.

Each of the three sauces has a min and max WASS, given in the table below.

Min WASS	Max WASS	Cooking Time (mins)	Bottling Time (mins)	Pre-orders (bottles)	Selling Price	Handling Cost
Mild	5	18	4	3	100	$10.00	$5.00
Fiery	40	70	5	3	75	$14.00	$9.00
Extreme	125	200	8	3	50	$20.00	$11.00

Each bottle requires 80g of peppers and the given cooking time and bottle time in minutes. Each bottle also incurs the given handling cost and can be sold for the given selling price.

DJ Mustard has 24 hours of cooking time available, 16 hours of bottling time available, and an unlimited amount of bottles.

DJ Mustard has already received pre-orders for his three sauces and has to make at least that many bottles. But he can make more, and will sell whatever he makes.

Formulate a linear program that will help DJ Mustard maximize his profit give the resources he has.

Consider the following decision variables:

Let Xij represent the kg of pepper i (i = J,S,H) blended into sauce j (j = M, F, E)

Let Yj represent the number of bottles of type j manufactured and sold (j = M, F, E)

Now answer the following questions about the formulation:

The following constraint is supposed to handle cooking and bottling time:

(4 + 3) * Y_M + (5 + 3) * Y_F + (8 + 3) * Y_E <= ( 1440 + 960 )

Is there anything wrong with it?

a	The constraint is correct
b	The coefficients are right, but the variables are not right
c	This constraint doesn't work, it needs to be replaced with two constraints: one for cooking time and one for bottling time
d	The right hand side should be in hours