Question

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.

Answer 1

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

Answer 2

Answer for this question.