Amanufacturer sells each of his tv sets for $85. the cost c (in dollars) of manufacturing and selling x tv sets per week is c = 1500 + 10x + 0.005x2. if at most 10,000 sets can be produced per week, how many sets should be made and sold to maximize the weekly profit?

7500 sets

Step-by-step explanation:

We are given that

Cost of each TV set=$85

The cost C(in dollars) of manufacturing  and selling x Tv sets per week is given by

Set can be produced at most per week=10000

We have to find the number of sets should be made and sold to maximize the weekly profit.

Revenue=85 x

Where x= number of sets selling per set

Profit=Revenue-Cost

Profit=85x-(1500+10x+0.005x^2)[/tex]

Profit=P=

Differentiate w.r.t x

Substitute

Again differentiate w.r.t x

Hence,function is maximize.

Therefore, 7500 sets should be made and sold to maximize the weekly profit.

The chances that it will not rain is:

                         80%

Step-by-step explanation:

We are given that:

The chances that it will rain tomorrow are 20%.

Let A denote the event that it will rain.

and A' denote the vent that it will not rain.

Let P denote the probability of an event.

We have:

P(A)=0.20

Hence,

P(A')=1-P(A)

P(A')=1-0.20

P(A')=0.80

which in percent is given by:

           P(A')=80%