Question

You are the owner of a company that produces and sells a new tool at hardware stores. During one month, when 'x' of those new tools were produced and sold, the following were the revenue and cost (in hundreds of dollars).  

R(x)= -0.06x² +13.12x + 65.8 C(x)=3.04x+ 7.6

5.Fill-in the blanks.Be sure to read the following carefully!

HINT: do NOT use the TABLE from your graphing calculator, but DO use the graphing capabilities.

a)The profit for that month was 79 hundred dollars when ..........................of the new tool were produced and sold.

b)The profit for that month was 98 hundred dollars when ...........................of the new tool were produced and sold.

c)The profit for that month was 316 hundred dollars when...........................of the new tool were produced and sold.

d)The profit for that month was 47,600 dollars when................................of the new tool were produced and sold.

Answer 1

Solution-

We have

Revenue function in hundred dollars

of x new tools sold as

....1

and Cost function in hundred dollars of x new tool produced as

C(x) = 3.04x + 7.6 ...........2

From 2 equatios, we get

The profit in hundred dollarsof x new tools sold is

P(x) = R(x) - C(x)

......3

(a) Profit=P(x)= 79 hundred dollars

Putting the value in equation 3, we get

Solving this quadratic equation we get

x= 167.26 and x=2.07

Negelecting small value , we get

The profit is 79 hundred dollars when 167 new tools are produced and sold.

(b) ProfotPP(x)= 98 hundred dollars

Putting the value in equation 3, we get

Solving this quadratic equation,we get

x=165.3 and x=4

Hence, proft is 98 hundred dollars when165 new tools are produced and sold.

(c)Profit=P(x)=316 hundred dollars

Putting the value in equation 3 , we get

Solving this equation, we get

x=138.2 and x=31

Hence, profit is 316 hundred dollars when 138 new tools are produced and sold.

(d) Profit=p(x) 47600 dollars=47.6 hundred dollars.

Putting the value in equation 3, we get

Solving the equation, we get

x=168.3 and x=1

Hence, profit is 47600 dollars when 168 tools are produced and sold.