question 16\na company that manufactures and sells gaming pcs has run some estimates of monthly costs and…

question 16\na company that manufactures and sells gaming pcs has run some estimates of monthly costs and sales. when their pcs are priced at p dollars per pc, they expect to sell d pcs that month, given by the demand - equation\n4p + 2d=16,400.\nthe total cost of manufacturing d pcs in a month is given by the function\nc(d)=225d + 15,400 dollars.\ngiven this information, how much does it cost the company to make one gaming pc on average, if 7,200 gaming pcs are made in a month? round your answer appropriately and enter it as just a numerical quantity (no labels or symbols).

question 16\na company that manufactures and sells gaming pcs has run some estimates of monthly costs and sales. when their pcs are priced at p dollars per pc, they expect to sell d pcs that month, given by the demand - equation\n4p + 2d=16,400.\nthe total cost of manufacturing d pcs in a month is given by the function\nc(d)=225d + 15,400 dollars.\ngiven this information, how much does it cost the company to make one gaming pc on average, if 7,200 gaming pcs are made in a month? round your answer appropriately and enter it as just a numerical quantity (no labels or symbols).

Answer

Explanation:

Step1: Identify the cost - function

The cost function is given as $C(D)=22D + 15400$, where $D$ is the number of PCs manufactured.

Step2: Substitute $D = 7200$ into the cost - function

When $D = 7200$, we have $C(7200)=22\times7200+15400$. First, calculate $22\times7200 = 158400$. Then, $C(7200)=158400 + 15400=173800$.

Step3: Calculate the average cost per PC

The average cost per PC, $\overline{C}$, is $\frac{C(7200)}{7200}$. $\overline{C}=\frac{173800}{7200}\approx24.14$.

Answer:

$24.14$