Acompany manufactures and sells x television sets per month. the monthly cost and price-demand equations are c(x)=72,000+60x and p(x)=300−(x/20),

0l≤x≤6000.

(a) find the maximum revenue.

(b) find the maximum profit, the production level that will realize the maximum profit, and the price the company should charge for each television set.

(c) if the government decides to tax the company $55 for each set it produces, how many sets should the company manufacture each month to maximize its profit? what is the maximum profit? what should the company charge for each set?

Following are the responses to the given question:

For point a:

for maximum revenue

maximum revenue:

For point b:

for maximum cost

Maximum profit = when were manufacture and solded for each.

For point c:

for maximum cost

In each taxed set at so, the maximum profit = . If 1850 sets are manufacture and sold as each .

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Step-by-step explanation:

Given

Cost Price

Price

Revenue generated

where x=no of units

To get maxima and minima differentiate R(x)

maximum Revenue

(b)Profit=Revenue - cost

differentiate Profit to get maximum value

maximum Profit

(c)Now company decided to tax the company $ 55 for each set

Profit

differentiate Profit to get maximum value

company should charge 207.5 $ for each set

a.

step-by-step explanation:

step 1 distribute 2 to every term in the parentheses

step 2 add 10 on both sides of the equal sign

37/3

step-by-step explanation:

step 1: simplify both sides of the equation.

7x+8(x+

1

4

)=3(6x−9)−8

7x+(8)(x)+(8)(

1

4

)=(3)(6x)+(3)(−9)+−8(distribute)

7x+8x+2=18x+−27+−8

(7x+8x)+(2)=(18x)+(−27+−8)(combine like terms)

15x+2=18x+−35

15x+2=18x−35

tep 2: subtract 18x from both sides.

15x+2−18x=18x−35−18x

−3x+2=−35

step 3: subtract 2 from both sides.

−3x+2−2=−35−2

−3x=−37

step 4: divide both sides by -3.

−3x

−3

=

−37

−3

x=

37

3