Problema Solution
smookers lumber can convert logs into either lumber or plywood. in a given day, the mill turns out three times as many units of plywood as lumber. it makes a profit of $25 on a unit of lumber and $40 on a unit of plywood. how many of each unit must be produced and sold in order to make a profit of $14645?
Answer provided by our tutors
THERE ARE 3 SOULTION HERE = SOULTION1= P=3L
40(3L)+25L=14790
145L=14790
L=102
P=3*102
P=306
SOULTION2= P = 14790 and we have:
x * l + y * p = P
Where x = 25, and y = 40:
25l + 40p = 14790
Now we know that p = 3l, so:
25l + 40(3l) = 14790
25l + 120l = 14790
145l = 14790
l = 102, so 102 lumber, and 102/3 or 34 plywood!
SOULTION3 P = # units plywood
L = # units lumber
Given constraint: P = 3L
$14,790 = $25L + $40P
But we know P in terms of L from the constraint so, substitute
14790 = 25L + 40(3L)
14790 = 25 + 120 = 145L
Divide both sides by 145
L = 328 2/3
Plug into original equation and solve for P
$14,790 = $25(328.66666)+ $40P
6573.35 = 40P
P = 164.334
Check: $40*164.334 + $25*328 2/3 = 14,790