A dietitian wishes to plan a meal around three foods. The meal is to include 21,

Question

A dietitian wishes to plan a meal around three foods. The meal is to include 21,070 units of vitamin A, 11,210 units of vitamin C, and 930 units of calcium. The number of units of the vitamins and calcium in each ounce of the foods is summarized in the table below. Determine the amount of each food the dietitian should include in the meal in order to meet the vitamin and calcium requirements. Food x oz X o2 X oz Food 11 Food III i Food II Food Vitamin A 430 8601290 Vitamin C 120 650 565 Calcium 902050

Explanation / Answer

Dear Student Thank you for using Chegg !! Given The meal should have following quantities of Vitanmins and Calcium Vitamin A = 21070 Vitamin C = 11210 Calcium = 930 Let the meal consist of x amount of Food1 , y amount of food 2 and z amount of Food 3. Hence as per quation comparing the actual mount of vitamin and calcium in the mean with required amount i.e. 430x + 860y + 1290z = 21070 (1) 120x + 650y + 565z = 11210 (2) 90x + 20y + 50z = 930 (3) Now using matrices we can deduce x,y,z as follows x 430 860 1290 21070 y = inv( 120 650 565 ) X 11210 z 90 20 50 930 Calculating inverse of matrix A 430 860 1290 B = inv( 120 650 565 ) 90 20 50 Computing adj(B) b11 = 21200 b12 = 44850 b13 = -56100 b21 = -17200 b22 = -94600 b23 = 68800 b31 = -352600 b32 = -88150 b33 = 176300 adj(B) = 21200 -17200 -352600 44850 -94600 -88150 -56100 68800 176300 det(B) = -24682000 inv(B) = (1/det(B))* adj(B) = -0.0008589 0.000697 0.01428571 -0.0018171 0.003833 0.00357143 0.00227291 -0.00279 -0.0071429 Now multiplying x 3 y = 8 z 10 Hence x=3 y = 8 z = 10 Solution

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