MHB Linear Programming Formulation problem faced - Maximization problem

AI Thread Summary
The discussion revolves around formulating a linear programming (LP) model for Company Y, which produces two types of cookies, S and E, with specific ingredient constraints. The company has limited daily supplies of flour, sugar, and chocolate, and must meet minimum ingredient percentages for each cookie type. The objective is to maximize revenue, with Cookie E priced at $25 per kg and Cookie S at $20 per kg. The user presents an initial formulation but seeks validation and assistance in refining it. The conversation emphasizes the importance of correctly defining the objective function and constraints to ensure an accurate LP model.
huiwangzi
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Hi All.

I am new here and I faced some issues in formulating the objective functions and constraints for the following scenario.

Could any kind souls assist in giving me some advices on how I can proceed to do so?


Company Y is producing two different cookies; S cookies and E cookies. The ingredients of both cookies are Flour, Sugar and Chocolate (and nothing else). The company Y has the daily supply of 100KG of Flour, 20KG of Sugar and 30 KG of Chocolate. The mixture for Cookie S must contain at least 10% of Sugar and 10% of Chocolate. The mixture for Cookie E must contain at least 20% of Sugar. Cookie E are sold at \$25 per KG and Cookie S are sold at \$20 per KG. Develop an LP formulation for Company Y to maximise their revenue from the sales of both cookies. You may assume Company Y can sell as much as cookies that they can produce.

I have come out with the following answer. However, I am not too sure if it is correct. Appreciate if anyone could help me solve my queries.

Let X1 = Sales of Cookies S from Company Y
Let X2 = Sales of Cookies E from Company Y

Max 20 X1 + 25 X2
s.t. 0.10 X1 + 0.20 X2 ≤ 20
0.20 X1 ≤ 30 Thank you!
 
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