This is really linear programming, not statistics.
p = 4 a + 6 b
That is the objective function we wish to maximize
1 a + 3 b </=240 wood constraint
3 a + 4 b </=360 plastic constraint
2 a + 1 b </=180 steel constraint
graph those three constraint lines with a on x axis and b on y axis
for w
intercepts to make that easy
wood (0,80) and (240,0)
plastic (0,90) and (120,0)
steel (0,180) and (90,0)
so
wood y = -x/3 + 80
plastic y = -3x/4 + 90
steel y = - 2x + 180
so corners (except 0,0 )
wood-plastic
-x/3 + 80 = -3x/4 + 90
5 x/12 = 10
x = 24 and y = 72
what is p there ?
p = 3*24 + 6*72
also
do that for the wood - steel
and for the plastic - steel
pick the biggest p
A manufacturer has a maximum of 240, 360, and 180 kilograms of wood, plastic and steel available. The company produces two products, A and B. Each unit of A requires 1, 3 and 2 kilograms of wood, plastic and steel respectively; each unit of B requires 3, 4 and 1 kilograms of wood, plastic and steel respectively. The profit per unit of A and B is $4.00 and $6.00 respectively.
a) Write out the objective profit function.
b) Write out the constraints this company faces.
c) List all corner points and determine which combination of items will produce the maximum profit.
2 answers
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