A biscuit manufacturing company plans to product two types of biscuits, one with

Question

A biscuit manufacturing company plans to product two types of biscuits, one with a round shape (Type 1) and another with a square shape (Type 2). The following resources are used in manufacturing the biscuits: raw material, machinery labor (man-hours). The resources used are shown in Table 1. If the unit profit of round and square biscuits is 3.00 euros and 2.00 euros respectively, how many round and square biscuits should be produced to maximize total profit?

Table 1) Resources Requirement/Unit Type 1Type 2 Resources Daily availability 100 Raw material Machine 115 12 1500 grams 720 minutes 240 minutes 10 LManpower a) b) c) Define the decision variables Transform problem in mathematical format Solve the problem using the graphical method

Explanation / Answer

The resources used are shown in Table 1:

Raw Material : Type 1= 1500 grams/100

1500 grams/115

The decision variables include raw material, machine manpower. How much raw material does one use toi produce Type 1 Biscuit.

So For Type 1 Biscuit the requiremnt would be 72 minutes

For Type 2 Biscults the requirement would be 60 minutes

Manpower: There would be 80 minutes of manpower for Type 1 Biscuit

There would be 120 minutes of manpower needed for Type 2 Biscuits.

Raw Material x (Number of Units)+ Machine x(Number of Units) + Manpower x Number of Units = Total Cost of the Type 1 Biscuit.

If profit is 3 Euros and 2 Euros.

Total Price is 10 Euros for Type 1 = Selling Price

Total Price is 20 Euros for Type 2= Selling Price

Total Maximum profit would be derived if the machines are utilized in full capacity.

They would be utilized in full capacity, and stocks are generated.

Suppose the quantity of stock is 72

Selling price is 3 Dollar

So the units that could maximize the profit is 72 Units for Type 1

For TYpe 2 Biscuits the requirement is 60 Units.

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