Answer now, 50 points!
a retailer has determined that the cost of ordering and storing x units is given by the equation c= 7x + (210,000 / x) where 1 ≤ x ≤ 100
the truck that transports them can carry at most 100 units. what is the number of units that must be ordered to minimize the cost

C' = 7-230000/x^2

Step-by-step explanation:

Min occurs when C'=0

0=7-230000/x^2

230000/x^2=7

230000=7x^2

32857.128 = x^2

181.265 = x

Out of range.

So the min must be at an endpoint.

C(1) = 7+230000 = 230007

C(100) = 700+2300 = 3000

Since C(100)<C(1), C(100) is the minimum on the interval [1, 100]

The order size that will minimize cost is 100 units.

(0,-3) see attached graph

step-by-step explanation:

a. to solve the system, graph the two equations.

x = y+3 becomes y=x-3 has m=1/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move up 1 unit and 1 unit to the right. plot a point and connect.

y=-4x+3 has m =-4/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move down four units and to the right 1 unit. plot a point and connect.

the solution is the point (x,y) where the two lines intersect. by the graph below it is (0,-3).

b. to solve by substitution, substitute y = -4x-3 into x= y+3

x= (-4x-3) +3

x=-4x

5x=0

x=0

now substitute x = 0 back in to find y.

y= -4(0)-3

y=0-3

y=-3

solution is (0,-3)

c. use elimination by adding the equations together.

x-y=3

4x+y=-3

5x=0

x=0

then substitute into one equation to find y.

y=-4(0)-3

y=-3