Question 1189901: 7. The top two dolls that a toy manufacturer makes are called Baby Wiggles and
Sleepy Baby. To make a case of Baby Wiggles takes 10 units of raw material
and I unit of time to assemble. To make a case of Sleepy Baby takes 6 units of
raw material and 2 units of time to assemble. On a given day the manufacturer
has at most 300 units of raw material and 44 units of time. If the manufacturer
makes a profit of $170 on each case of Baby Wiggles and $140 on each case
of Sleepy Baby, how many cases of each type of doll should the manufacturer
make in order to maximize profit?
Found 2 solutions by Theo, ikleyn:
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! x = the number of cases of baby wiggles
y = the number of cases of sleepy baby.
baby wiggles takes 10 units of raw material and 1 unit of time to assemble.
sleepy baby takes 6 units of raw material and 2 units of time to assmble.
on a given day, the manufacturer has at most 300 units of raw materials and 44 units of time available.
the manufacturer makes a profit of 170 on each case of baby wiggles and 140 on each case of sleepy baby.
your constraint inequalities are:
10x + 6y <= 300
x + 2y <= 44
x >= 0
y >= 0
your objective function is:
profit = 170 * x + 140 * y
using the desmos.com calculator, you would graph the opposite of the constraints and then evaluate the objective function at the corner poinjts of the feasible region.
the feasible region is the area on the graph that is not shaded.
here's what the graph looks like.
all constraints need to be met.
at the maximum profit point of (24,10), .....
10x + 6y = 240 + 60 = 300 which is <= 300
x + 2y = 24 + 20 = 44 which is <= 44.
this confirms all the constraints are met.
your maximum profit is when 24 cases of baby wiggles and 10 cases of sleepy baby are manufactured and sold.
Answer by ikleyn(52787)  (Show Source):
You can put this solution on YOUR website! 7. The top two dolls that a toy manufacturer makes are called Baby Wiggles and
Sleepy Baby. To make a case of Baby Wiggles takes 10 units of raw material
and I unit of time to assemble. To make a case of Sleepy Baby takes 6 units of
raw material and 2 units of time to assemble. On a given day the manufacturer
has at most 300 units of raw material and 44 units of time. If the manufacturer
makes a profit of $170 on each case of Baby Wiggles and $140 on each case
of Sleepy Baby, how many cases of each type of doll should the manufacturer
make in order to maximize profit?
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I'd like to make a notice to a person who created this problem (to the problem's composer).
The problem is worded unnatural, when it says
"On a given day the manufacturer has at most 300 units of raw material".
According to this formulation, the manufacturer may have 200, or 100 or 50 units of raw material
at that particular day, but the reader CAN NOT know, what the manufacturer really has.
The correct formulation is
(1) "On a given day the manufacturer has  300 units of raw material".
Or in this way
(2) "On a given day the manufacturer may use at most 300 units of raw material".
Then the problem acquires a clear sense and a harmonious sounding.
You may ask, how in formulation (1) the inequality sign appears in constrains ?
The answer is very simple: because, having 300 units of the rowing material, the manufacturer
may use not full amount.
Again, as presented, the problem formulation is defective and should be fixed.
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