Your friend Jeremy is planning to start a new business producing and distributing nutrition bars in Cambridge. After some market research and several tasting runs, he has created four types of nutrition bars, as shown in Table 1. Each bar requires different amounts of protein powder and sugar.

The current cost per gram of protein powder is $0.23 and the cost per gram of sugar is $0.34. The monthly demand for bars in the area is estimated in 1500 units in total (considering any and all types of bars).

Jeremy asked for your help to determine the quantity of each nutrition bar type to produce to ensure the lowest cost while fulfilling the demand.

Table 1: Protein powder and sugar per type of bar

Type of Bar	Protein Powder (in grams)	Sugar (in grams)
Soy	6	9
Nuts	9	4
Yogurt	6	9
Peas	12	3

What would be the minimum cost (in $) to fulfill the monthly demand?

Round your answer to the nearest integer.

Question 2

The next step in this process is to identify the best supplier for each ingredient. Jeremy requested Melissa, his best friend who gained some experience in procurement after a recent internship, to contact some well-known suppliers, select one of them, and confirm their estimated costs.

After a few phone calls, Melissa decided to choose Supplier A, whose costs of sugar and protein powder per gram are the same as the information provided in Question 1. The expected monthly demand also remains unchanged from Question 1. However, theres a monthly capacity limitation for the supplier to source these ingredients.

Table 2: Supplier's capacity per month

Ingredients	Capacity (in grams)
Protein Powder	12000
Sugar	10000

Adjust the model from Question 1. Whats the minimum cost (in $) to fulfill the expected monthly demand considering Supplier A's capacity constraint? Keep in mind that you can use any type and combination of nutrition bars to fulfill the demand.

Round your answer to the nearest integer.

Question 3

The government is considering a new regulation that will require the implementation of special warehousing facilities for Soy, Nuts, and Yogurt nutrition bars. These facilities can be used at the following monthly rates: $1000 for Soy, $200 for Nuts, and $300 for Yogurt nutrition bars. Jeremy requested you evaluate the impact of this regulation on costs.

Adjust your model from Question 2. What would be the new minimum cost (in $) to fulfill the expected monthly demand if the new regulation is implemented?

Round your answer to the nearest integer.

Question 4

Finally, the government has decided not to implement the new regulation, so you can disregard the analysis from Question 3.

After extensive research, Jeremy developed a new recipe for nutrition bars to improve the flavor and texture. This recipe requires the use of a specific type of protein powder for each type of nutrition bar. Each type of protein powder has a different cost and availability (see Table 3). Jeremy would like you to adjust the model from Question 2 to produce protein bars using the new recipe while minimizing costs.

Table 3: Costs (in $ per gram) and availability (in grams) of protein powder for each nutrition bar type

Type of bar	Cost per gram of protein powder (in $)	Availability of protein powder (in gram)
Soy	0.29	3500
Nuts	0.36	2500
Yogurt	0.44	4000
Peas	0.18	5000

Using the costs and availability of protein powder presented in Table 3, what would be the new minimum cost (in $) to fulfill the expected monthly demand?

Round your answer to the nearest integer.

Kindly provide answers to it