A company produces two types of solar panels per year: x thousand of type A and y thousand from type B. The revenue and costs equations, in millions of dollars, for the year given as follows R(x, y) = 5x+3y
c(x, y) = x2 -3xy+8y2 +11x-52y-3
Determine how many soalr panels of each type should be produced per year to maximize profit.
The company will achieve a maximum profit by selling (X) solar panels of type A and selling (X) solar panels of type B.

The  profit is

 The  number of solar panels of type a is  3 thousand

   The number of solar panels of type B is  4 thousand

Step-by-step explanation:

From the question we are told that

  The  revenue function is  

  The  cost function is

Generally the profit function is mathematically represented as

Now the next step is to differentiate the profit function partially

At maximum or minimum so

and  

So

Solving equation 1 and 2 simultaneously using substitution method

      From 1

substituting this to 2

multiply through by 2

=>  

So

So the critical point is   (v,w) =  (3, 4)

Now differentiating  partially and substituting the critical point s we have

Now differentiating  partially and substituting the critical point s we have

Now to determine whether the obtained critical point is maximum or minimum the expression

      must be greater than zero so

So \

The maximum price is mathematically evaluated as

So

 The  number of solar panels of type a is  3 thousand

   The number of solar panels of type B is  4 thousand

by definition, an arc subtended by a central angle of some given measure has the same measure. so .

m∠cdf = 43° , m∠gdf = 114°, m∠gde = 23°, m∠edh = 23° , m∠cdh = 157°

step-by-step explanation:

since, it is given that de bisects the angle gdh ⇒ de divides the angle gdh into two equal angles.

⇒ m∠gde = m∠edh

⇒ 8·x   - 1 = 6·x + 5

⇒ x = 3

so, m∠gde = 8·x - 1 = 23°

and m∠edh = 23°

now, it is given ∠cde is an straight angle so, m∠cde = 180°

⇒ m∠cdf + m∠fdg + m∠gde = 180°

⇒ 43° + m∠fdg + 23° = 180°

⇒ m∠fdg = 114°

again, m∠cde = m∠cdh + m∠edh = 180°

m∠cdh + 23° = 180°

⇒ m∠cdh = 157°