MATH

Kane Manufacturing has a division that produces two models of fireplace grates, x units of model A and y units of model B. To produce each model A grate requires 3 lb of cast iron and 6 min of labor. To produce each model B grate requires 4 lb of cast iron and 3 min of labor. The profit for each model A grate is $3.50, and the profit for each model B grate is $4.00. Also, 1000 lb of cast iron and 20 labor-hours are available for the production of fireplace grates per day.

Because of a backlog of orders for model A grates, Kane's manager had decided to produce at least 150 of these grates a day. Operating under this additional constraint, how many grates of each model should Kane produce to maximize profit?
x,y=
What is the optimal profit?

  1. 👍
  2. 👎
  3. 👁
  1. What are the constraints?
    x+y >= 150
    x >= 0
    y >= 0
    3x + 4y <= 1000
    6x + 3y <= 20*60
    You want to maximize
    p = 3.50x + 4.00y

    So now solve in the usual way. Graph the region and evaluate p(x,y) at each vertex. There are several good linear algebra calculator web sites online.

    1. 👍
    2. 👎

Respond to this Question

First Name

Your Response

Similar Questions

  1. science

    Why do scientists use models? a. Scientists use models to learn about things that are too small, too large, or too complex to observe directly. b. Scientists use models because doing so is always part of the scientific method. c.

  2. Science

    Q1: Why do scientist use models? A.) Scientist use models to learn about things that are too small, too late, or too complex to observe directly. B.) Scientist use models because doing so is always part of the scientific method.

  3. Statistics

    A manufacturer makes two models of an item: model I, which accounts for 80% of unit sales, and model II, which accounts for 20% of unit sales. Because of defects, the manufacturer has to replace (or exchange) 10% of its model I

  4. finite math

    Kane Manufacturing has a division that produces two models of hibachis, model A and model B. To produce each model-A hibachi requires 3 lb of cast iron and 6 min of labor. To produce each model-B hibachi requires 4 lb of cast iron

  1. Math - Linear Inequalities

    The Wellbuilt Company produces two types of wood chippers, Deluxe and Economy. The Deluxe model requires 3 hours to assemble and ½ hour to paint, and the Economy model requires 2 hours to assemble and 1 hour to paint. The maximum

  2. math

    The estimated monthly profit (in dollars) realizable by Cannon Precision Instruments for manufacturing and selling x units of its model M1 digital camera is as follows. p(x)=-0.07x^2+322x-96,000 To maximize its profits, how many

  3. business math

    National Business Machines manufactures x model A portable printers and y model B portable printers. Each model A costs $100 to make, and each model B costs $150. The profits are $40 for each model A and $35 for each model B

  4. The Graphical Method

    A manufacturer produces two models of mountain bikes. Model A requires 5 hours of assembly time and 2 hours of painting time, and Model B requires 4 hours of assembly time and 3 hours of painting time. The maximum total weekly

  1. pre cal

    The vector u = (4300, 5200) gives the number of units of two models of laptops produced by a company. The vector v = 1800, 1200 gives the prices (in dollars) of the two models of laptops, respectively. Identify the vector

  2. finite

    Kane Manufacturing has a division that produces two models of hibachis, model A and model B. To produce each model A hibachi requires 6 lb of cast iron and 12 min of labor. To produce each model B hibachi requires 7 lb of cast

  3. ACCOUNTING

    Gardner Manufacturing Company produces a product that sells for $120. A selling commission of 10% of the selling price is paid on each unit sold. Variable manufacturing costs are $60 per unit. Fixed manufacturing costs are $20 per

  4. Math

    Salim sells fax machines that come in Standard and Enhanced models. The Standard model sells for $325 and the Enhanced model sells for $385. If Salim sold a total of 35 units and took in $12,575, how many of the Enhanced model did

You can view more similar questions or ask a new question.