linear programming

Quote:

Originally Posted by gracy

question::A manufacturer of ovens must ship atleast 100industrial ovens to its west coast warehouses.Each warehouse holds a maximum of 100 ovens.
warehouse A already has 25 ovens in storage and warehouse B has 20.Itcost $12 to ship an oven to warehouse a and $10 to ship one to warehouse B.union rule requires that atleast 300 workers ahould be hired.shippinh an oven to warehouse A requires 4 workers,while shipping oneto warehouse B requires 2 workers
(a) how many ovens should be shipped to each warehouse to minimize cost
(b)what is minimum cost

Hello,

number of ovens shipped to A: x
number of ovens shipped to B: y

Then you can extract the following inequalities from your problem (I've copied the corresponding text from your problem):
$x+y\leq 100\ \Longrightarrow\ y\leq-x+100$ ...A manufacturer of ovens must ship atleast 100industrial ovens...(black line)
$0\leq x\leq75$ ...warehouse A already has 25 ovens...(green line)
$0 \leq y\leq80$ ...warehouse B has 20...(green line)
$4x+2y\leq 300\ \Longrightarrow \ y\leq -2x+150$ ...union rule requires that atleast 300 workers ahould be hired.shippinh an oven to warehouse A requires 4 workers,while shipping oneto warehouse B requires 2 workers...(blue line)

I've sketched these inequalities. They form the circumference of the grey area.

The costs of the shipping can be described by the function:
$c = 12x+10y\ \Longrightarrow\ y=-\frac{6}{5}x+\frac{c}{10}$

To minimize the costs the y-intercept of this line must be small. You'll get the best result if you ship 20 ovens to A and 80 ovens to B. Then the costs will be 1,040 $. I've sketched the optimal cost function (red line)

To calculate the minimal costs plug in x = 20 and y = 80 into $c = 12x+10y$

EB