Question 2 (25 points) Dr. Garcia has decided to open a bakery with her best fri

Question

Question 2 (25 points) Dr. Garcia has decided to open a bakery with her best friend that will be open only on the weekends. After some initial research, they have determined what the estimated demand for their products will be, how much they will need to spend on supplies per batch of baked goods, and what the prices will be. This data is included in the tables below. Cupcake Muffin Scone Cookie Min Weekend Demand Max Weekend Demand Sale Price Per Item Sold 300 500 200 600 100 300 50 200 4 Demand and Sale Price Data # Items Per Batch | Cost of Ingredients Per Batch Cupcake Muffin Scone Cookie 12 6 24 Batch Size and Cost to Produce Each Batch They have decided to spend no more than $500 on baking supplies each week. Formulate an LP using the exact problem data to decide what their baking plan should be for the next three weeks Clearly define your variables, and write the objective and constraints in words and then give the mathematical formulation using the complete problem data (not in general form)

Explanation / Answer

Demand Variables

100 <= d1 (Cupcake) <= 300

300 <= d2 (Muffin) <= 500

50 <= d3 (Scone) <= 200

200 <= d4 (Cookie) <= 600

Let the number of batches for Cupcake, Muffin, Scone and Cookie be n1, n2, n3 and n4 respectively.

Since, the total spend should not exceed more than $500.

Therefore, cost equation would be as below:

8*n1+5*n2+6*n3+6*n4 <= 500

Where,

                d1 >= 12*n1

                d2 >= 12*n2

                d3 >= 8*n3

                d4 >= 24*n4

Sales equation will be as below and we need to maximize the sales in order to make maximum profit:

                Sale = 4*d1+2*d2+3*d3+1*d4

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