Patches is a cat who cats cat food for breakfast. Patches requires a breakfast diet that includes at least 40g of protein, at least 90gof iron but no more than 144g of carbs a week. His two favourite brands are Kitty Kibble and Cat Snack. Kitty Kibble contains Ig of protein, 11g of iron and 6g of carbohydrates per box. Cat Snack contain 5g of protein, 5g of iron and 6g of carbs per box. Kitty Kibble costs $4 a box, Cat Snack costs $2 a box. Patches' owner wants to minimise how much money they spend on cereal while meeting Patches' dietary requirements. 1. Construct a table showing: the number of the elements required for each item the amount of each element available or the minimum requirements of each element. 2. State the objective function and determine the constraints for each element. 6. ● ● 7. 3. Item Kitty Kibble Cat Snack Minimum Maximum Objective Function: Let x represent the brand of Kitty Kibble. Let y represent the brand of Cat Snack. 4. Produce a labelled graph showing the feasible region. (0,01) (38) 9 Protein (g) 1 5 40 B (1) (57) Iron (g) Carbohydrates (g) Cost ($/box) 11 6 5 90 Ex+ys144 (PL) Therefore, the objective function will be: Minimise = 4x + 2y x+5y2 40 Find the optimal solution by considering the feasible points. the minimum value of the objective function is 34 at the point (5,7). Hence, the optimal solution by considering the feasible points x = 5, y = 7 and min 2 = 34 is: (0) 6 - 144 A (0,24) B (0,18) C (5,7) D (20,4) Determine the wastage or oversupply of elements for the optimal solution. 5. Corner Point 4 2 - Z = 4x + 2y ZA= 4(0) + 2(24) = 0+48= 48 Za = 4(0) + 2(18)= 0+36 = 36 Zc=4(5) +2(7)=20+14=34 Zp=4(20) + 2(4) = 80 +8 = 88