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Preview File Edit View Go Tools Window Help s Adelphi Math Concepts Linear Programming- Dec 14 2017pdf (1 page) Q Search 4. Using the matrix below, answer the following questions Product A Product B Productvaiable 1.5 700 hours 857900 gallons 800 pounds Hours required to make one of each product 43.5 Gallons of water required to make one of each product5 Pounds of materials required to make one of each product $20 Retail price when selling one of each product$30$33 $22 $35 Cost to make one of each product $18 o What is the linear program for cost? o What is the linear program for revenue? o What is the linear program for profit? o What is the linear program for revenue if no one product can be more than half of all products made? o What is the linear program for revenue if there must be at least 100 gallons of left over water? o What is the linear program for revenue that uses all the hours?

Explanation / Answer

In total there are 3 products that are being manufactured namely A,B,C ;
Let number of produced units of product A be 'a' and similarly 'b' for product B and 'c' for product C;

Linear program for cost will be a sum of the individual prices and production quantities. Given by:
18a + 20b + 22c

Linear program for revenue will be a sum of the individual revenues and production quantities. Given by:
30a + 33b + 35c

Linear program for profit would be the differences in revenues and costs given by :
= (30a + 33b + 35c) - (18a+20b+22c)
= 12a + 13b +13c

Linear program for revenues in this case will be the same, with an added constraint
30a + 33b + 35c such that a <= (a+b+c)/2, b<= (a+b+c)/2 and c<= (a+b+c)/2

Linear program for revenue with 100 gallons of left over water would be
30a + 33b + 35c such that 8a+5b+7c <= (900-100) = 800
30a + 33b + 35c such that 8a+5b+7c <= 800

Linear program for revenue that uses all the hours :
30a + 33b + 35c such that 4a+3.5b + 1.5c = 700

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