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.

Question

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?

Damon · Answer

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
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2 w = 400
w = 200
g = 300 so (300,200)
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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)