Tyler Clark - Homework 2 ECON

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Feb 20, 2024

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Tyler Clark – ECON Homework 2 2.11. The WorldLight Company produces two light fixtures (Products 1 and 2) that require both metal frame parts and electrical components. Management wants to determine how many units of each product to produce per week so as to maximize profit. For each unit of Product 1, one unit of frame parts and two units of electrical components are required. For each unit of Product 2, three units of frame parts and two units of electrical components are required. The company has a weekly supply of 3,000 units of frame parts and 4,500 units of electrical components. Each unit of Product 1 gives a profit of $13, and each unit of Product 2, up to 900 units, gives a profit of $26. Any excess over 900 units of Product 2 brings no profit, so such an excess has been ruled out. D. Formulate this same model algebraically. 2.11d. 3x + 2y < 3000 x + 2y < 4500 y < 900 13x + 26y = P See graph on scratch paper 2.23. Dwight is an elementary school teacher who also raises pigs for supplemental income. He is trying to decide what to feed his pigs. He is considering using a combination of pig feeds available from local suppliers. He would like to feed the pigs at minimum cost while also making sure each pig receives an adequate supply of calories and vitamins. The cost, calorie content, and vitamin content of each feed is given in the table below. Contents Feed Type A Feed Type B Calories (per pound) 800 1,000 Vitamins (per pound) 140 units 70 units Cost (per pound) $0.40 $0.80 Each pig requires at least 8,000 calories per day and at least 700 units of vitamins. A further constraint is that no more than 1/3 of the diet (by weight) can consist of Feed Type A, since it contains an ingredient that is toxic if consumed in too large a quantity. D. Formulate this same model algebraically. 2.23d. overall cost is $11.60 a day (see scratch paper)

3.1. Reconsider the Super Grain Corp. case study as presented in Section 3.1. The advertising firm, Giacomi & Jackowitz, now has suggested a fourth promising advertising medium—radio commercials—to promote the company’s new breakfast cereal, Crunchy Start. Young children are potentially major consumers of this cereal, but parents of young children (the major potential purchasers) often are too busy to do much reading (so may miss the company’s advertisements in magazines and Sunday supplements) or even to watch the Saturday morning programs for children where the company’s television commercials are aired. However, these parents do tend to listen to the radio during the commute to and from work. Therefore, to better reach these parents, Giacomi & Jackowitz suggests giving consideration to running commercials for Crunchy Start on nationally syndicated radio programs that appeal to young adults during typical commuting hours. Giacomi & Jackowitz estimates that the cost of developing each new radio commercial would be $50,000, and that the expected number of exposures per commercial would be 900,000. The firm has determined that 10 spots are available for different radio commercials, and each one would cost $200,000 for a normal run. C. Express this model in algebraic form. 3.1c. Cost – 50,000x Exposures – 900,000x Airing cost – 200,000x x <= 10 (all for each commercial) 3.16.*The Medequip Company produces precision medical diagnostic equipment at two factories. Three medical centers have placed orders for this month’s production output. The following table shows what the cost would be for shipping each unit from each factory to each of these customers. Also shown are the number of units that will be produced at each factory and the number of units ordered by each customer. A decision now needs to be made about the shipping plan for how many units to ship from each factory to each customer. C. Summarize this formulation in algebraic form.

3.16c. x 11 + x 12 + x 13 = 400 X 21 + x 22 + x 23 = 500

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