Larry decides to feed his dogs a combination of two dog foods. Dog food A contai

Question

Larry decides to feed his dogs a combination of two dog foods. Dog food A contains 4 units of protein, 1 unit of carbohydrates, and 2 units of fat and costs 80 cents. Dog food B contains 1 unit of protein, 1 unit of carbohydrates, 4 units of fat, and costs 60 cents. Larry feels that each day the dogs should have at least 6 units of protein, 4 units of carbohydrates, and 10 units of fat. How many units of dog food A and B should be given to the dogs to provide the minimum requirements at the least cost?

Explanation / Answer

Food A ---4P , 1C , 2F ; Costs --- 80cents

Food B ----P , 1C , 4F ; Costs ---- 60 cents

Least requirement --6P, 4C , 10F

Let x units of food A and y units of food B

Cost function : 80x +60y

Equations 4x+ y = 6-----(1)

x+y = 4 ------(2)

2x+ 4y =10 ------(3)

Solution of 1 and 2 gives 2/3, 10/3 ; Cost 2*80/3 + 10*60/3 = 253.33$

Solution of 1 and 3 gives 1 ,2 ; Cost 1*80 + 2*60 = 200

Solution of 2 and 3 gives 3, 1 ;Cost 3*80 + 1*60 = 300

Cost function is minimu for A( x) =1 and B(y )=3 an it meets the minium requirements of nutrition

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