Google Wants To Enter Your Home and Take Your Temperature

new revenue will be $f(n) = (7000*n + 1000000) * (249 - n)$ , where n is dollars decreased. Now, to find maximum, we can say $df/dn = 0$ . This would give n = 53 approximately. From given option 199 is nearest. At that price point, Google can earn a lot if you count!

Let f(x) be Google's revenue as a function of x and x be the # of dollars to decrease the price by.

$f(x) = (249 -x) (1,000,000 + 7,000x) \\$

$\frac{\mathrm d}{\mathrm d x} \left( f(x) \right) = 743,000 - 14,000x \\$

$743,000 - 14,000x = 0 \quad \to \quad 743,000 = 14,000x \quad \to \quad x \approx 53 \\$

$Price = 249 - 53 = \$196$

The ideal price to sell would be $196, the total revenue gets smaller as you move away from this figure. The closest price to the ideal is $199 which is our answer for the problem

As this question is MC it's easy. Sub the values 199, 99, 149 and 229 into the formula: $X\times[1000000+7000\times(249-X)]$

99 --> 202950000

149 --> 253300000

199 --> 268650000

229 --> 261060000

Clearly 199 would give Google the largest amount of revenue.

My answer is also 196, but by another method:

Given that for every unit increase in price, the demand falls by 7000. Hence at price zero, demand will be:

$1,000,000 + (7000*249) = 2,743,000.......................(1)$

Let Q denote demand and P, the price. Therefore, revenue will be PQ.

From eq (1) above and the given conditions,

$Q = 2,743,000 - 7000P$

$\rightarrow PQ = 2,743,000P - 7000P^2$

$\rightarrow dPQ/dP = 2,743,000-14000P$

Setting, $dPQ/dP = 0$ in order to find the maximum:

$2,743,000-14000P = 0$

$\rightarrow P= \frac{2,743,000}{14000} = 195.93 \approx \boxed{196}$

If $x$ is the number if dollars they drop the price, then $(10^6+7000x)(249-x)$ is their yearly revenue. We can complete the square (no calculus) to get that the maximum occurs at $x=743/14$ , so the price should be set at $249-743/14\approx\boxed{199}$ .

Just maximize the cost...u will get x=50...