1)The American Sausage Company (ASC) makes sausage in 1000 pound batches. The in
ID: 449714 • Letter: 1
Question
1)The American Sausage Company (ASC) makes sausage in 1000 pound batches. The ingredients are beef, filler (including spices) and preservatives. Ingredient costs are as follows: beef costs $2.50 per pound, filler costs $1.20 per pound and preservatives cost $1.80 per pound. Government regulations require the product to have at least 60% beef, no more than 20% filler and at most 5% preservatives. However, to maintain freshness, the company must add at least 1% preservatives. The company’s problem is to find the optimal mix of ingredients (in pounds) that minimizes the cost of making a batch of sausage, using linear programming (LP).. Answer the following questions: (a) Write down all decision variables. (b) Write down the objective function. (c) Write down all constraints.Explanation / Answer
(a) Write down all decision variables.
Decision variables –
X1 – qty of beef per 1000 pound of sausage
X2 – qty of filler per 1000 pound of sausage
X3 – qty of preservatives per 1000 pound of sausage
(b) Write down the objective function.
Minimize: 2.5X1 + 1.2X2 + 1.8X3
(c) Write down all constraints.
X1 + X2 + X3 = 0
X1 >= 1000*60%
X2 <= 1000*20%
X3 >= 1000*1%
X3 <= 1000*5%
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