Some years ago it was estimated that the demand for steel approximately satisfied the equation p equals 201 minus 20 x, and the total cost of producing x units of steel was Upper C (x )equals 153 plus 41 x. (The quantity x was measured in millions of tons and the price and total cost were measured in millions of dollars.) Determine the level of production and the corresponding price that maximize the profits.

The level of production is 4 units and the corresponding price that maximize the profits is $121.

Step-by-step explanation:

Since we have given that

the demand for steel would be

Total cost of producing x units of steel would be

Profit = R(x)-C(x)

So, it becomes,

First we derivative w.r.t to x we get that

Now, we will find the critical points,

So, now second derivative w.r.t. x.

We get that

So, there will be maximum profit at 4 units of level of production  and the corresponding price that maximize the profit would be

Hence, the level of production is 4 units and the corresponding price that maximize the profits is $121.

$4034.40

the perimeter of the field is the sum of the lengths of the four sides:

47 yd + 158 yd + 47 yd + 158 yd = 410 yd

the cost of 3 ft (1 yd) of fence is 3×$3.28 = $9.84.

so the cost of jake's wood perimeter fance is

(410 yd) × ($9.84 /yd) = $4034.40