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Problema 3.1-7 a y b Tomado del libro de Hillier y Liberman 7a Edición. The Apex Television Company has to decide on the number of 27 and 20-inch sets to be produced at one of its factories. Market research indicates that at most 40 of the 27-inch sets and 10 of the 20-inch sets can be sold per month. The maximum number of work-hour available is 500 per month. A 27-inch set requires 20 work-hours and 20-inch set requires 10 work-hours. Each 27-inch set sold produces a profit of $120 and each 20-inch ser produces a profit of $80. A wholesaler has agreed to purchase all the television sets produced if the number not exceed the maxima indicated by the market research. a) Formulate a linear programming model for this problem. b) Use the graphical method to solve this model. Problema 3.1-9 a y b Tomado del libro de Hillier y Liberman 7a Edición. The Primo Insurance Company is introducing two new product lines: special risk insurance and mortgages. The expected profit is $5 per unit on special risk insurance and $2 per unit on mortgages. Management wishes to establish sales quotas for the new product lines to maximize total expected profit. The work requirements are as follows:

Department Underwriting Administration Claims

Work-hours per unit Special Risk Mortgages 3 0 2

2 1 0

Work-hours Available 2400 800 1200

a) Formulate a linear programming model for this problem. b) Use the graphical method to solve this problem Problema 3.2-1 a y b Tomado del libro de Hillier y Liberman 7a Edición. The following table summarizes the key facts about two products A and B, and the resources, Q, R and S, required to produce them. Resource Usage per Unit Produced Resource Product A Product B Amount of Resource Available Q 2 1 2 R 1 2 2 S 3 3 4 Profit per Unit 3 2 All the assumptions of linear programming hold. a) Formulate a linear programming model for this problem. b) Solve this model graphically. Problema 3.4-7 Tomado del libro de Hillier y Liberman 7a Edición. Ralph Edmund loves steaks and potatoes. Therefore, he has decided to go on a steady diet of only these two foods (plus some liquids and vitamin supplements) for all his meals. Ralph realizes that this isn’t the healthiest diet, so he wants to make sure that he eats the right quantities of the two foods to satisfy some key nutritional requirements. He has obtained the following nutritional and cost information.

Ingredient Carbohydrates Protein Fat Cost per serving

Grams of Ingredient per Serving Steak Potatoes 5 15 20 5 15 2 $4 $2

Daily Requirement 50 40