math

A company is planning to purchase and store two items, gadgets and widgets. Each gadget costs $2.00 and occupies 2 square meters of floor space; each widget costs $3.00 and occupies 1 square meter of floor space. $1,200 is available for purchasing these items and 800 square meters of floor space is available to store them. Each gadget contributes $3.00 to profit and each widget contributes $2.00 to profit.
Identify all constraints.
Identify all applicable corner points of the feasibility region.
What combination of gadgets and widgets produces maximum profit?

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  1. contraints
    2 g + 3 w < 1200
    2 g + w < 800
    objective
    p = 3 g + 2 w

    corners (g,w)
    (0,0)
    if g = 0
    w = 400 or 800, use 400 (0,400)
    (0,400)
    if w = 0
    g = 600 or 400, use 400 (400,0)
    intersection
    2 g + 3 w = 1200
    2 g + w = 800
    ------------------
    2 w = 400
    w = 200
    g = 300 so (300,200)
    -------------------------------
    look at p
    at (0,0) is 0
    at (0,400) is 800
    at (400,0) is 1200
    at (300,200) is 3*300+2*200 = 1300
    max profit of 1300 at (300,200)

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