Question

only #3 please

2. The Munchies Cereal Company makes a cereal from several ingredients. Two of the ingredients, oats and rice, provide vitamins A and B. The company wants to know how many ounces of oats and rice it should include in each box of cereal to meet the minimum requirements of 48 mil- ligrams of vitamin A and 12 milligrams of vitamin B while minimizing cost. An ounce of oats contributes 8 milligrams of vitamin A and 1 milligram of vitamin B, whereas an ounce of rice contributes 6 milligrams of A and 2 milligrams of B. An ounce of oats costs $0.05, and an ounce of rice costs $0.03. a. Formulate a linear programming model for this problem. b. Solve this model by using graphical analysis. 3. What would be the effect on the optimal solution in Problem 2 if the cost of rice increased from $0.03 per ounce to $0.06 per ounce?

Answer 1

8x+6y> 48 X+2y>=12 A X> 0 2 2 8 10 C 12

The Jrey shaded area is the beosible aegion. The minimum will occun at erthen eb the Extoerme Point A,B ac A [9.4,4.8) B o8] D12,0]

The Cast to one aunce d oats is $0.05 0ond Cost o one ounce o auce is $0.0 (note that 40.03). Falmulate the lincan EcdiSarlier it wos Priogramming medel i mininising e cabt below obiective hnchan 0.05 2,t0.06 Z min ZA 0.05 (9.4) to.06 (ue) $0.408 ZA 7B 0.05 (0)+o. 06(e) ZBo.u80 Ze 0.05 (12) t0.06 (0) 2c 0.600 Now minimum occuns at A 3.44.8 -1