INEAR PROGRAMMING: MODEL FORMULATION AND GRAPHICAL SOLUTION

Problems

In Problem $40$ in Chapter $1,$ when Tracy McCoy wakes up Saturday morning, she reme that she promised the PTA she would make some cakes and$/$or homemade bread for its ba that afternoon. However, she does not have time to go to the store to get ingredients, and only a short time to bake things in her oven. Because cakes and breads require different temperatures, she cannot bake them simultaneously, and she has only $3$ hours available A cake requires $3$ cups of flour, and a loaf of bread requires $8$ cups; Tracy has $20$ cups A cake requires $45$ minutes to bake, and a loaf of bread requires $30$ minutes. The PTA a cake for $$10$ and a loaf of bread for $$6.$ Tracy wants to decide how many cakes and bread she should make.

a$.$ Formulate a linear programming model for this problem.

b$.$ Solve this model by using graphical analysis.

The Munchies Cereal Company makes a cereal from several ingredients. Two of the in oats and rice, provide vitamins A and B$.$ The company wants to know how many oun and rice it should include in each box of cereal to meet the minimum requirements ligrams of vitamin A and $12$ milligrams of vitamin B while minimizing cost. An our contributes $8$ milligrams of vitamin A and $1$ milligram of vitamin $B,$ whereas an ou contributes $6$ milligrams of A and $2$ milligrams of $B.$ An ounce of oats costs $$0\mathrm{.}05,$ an of rice costs $$0\mathrm{.}03.$

a$.$ Formulate a linear programming model for this problem.

b$.$ Solve this model by using graphical analysis.