Mark spends $20 * 1,000 shares = $20,000. When the stock price increases to $25/share, he makes ($25 – $20) * 1,000 shares = $5,000. 

$5,000 / $20,000 = \(\displaystyle \dpi{100} \small \frac{1}{4}\) = 25%

He does NOT increase his money by 125%, which would mean an additional $25,000, not $5,000.

Mary makes $13/hour and works 40 hours.  So she makes

\(\displaystyle \$13\cdot 40\ hours=\$520\). 

However, we need to subtract the cost of the items that she bought.  If the sweater retails for $50, Mary buys it for \(\displaystyle .75\cdot \50=\$37.50\) because of her 25% discount.  Similarly, she buys the jacket for \(\displaystyle .75\cdot 144=\$108\).  So her net profit is

\(\displaystyle 520-37.50-108=\$374.50\).

\(\displaystyle P(x)=500x-10,000\)

\(\displaystyle P(x)=500(100)-10,000\)

\(\displaystyle P(x)=50,000-10,000\)

\(\displaystyle P(x)=40,000\)

First of all, we need to know that

\(\displaystyle Gross\ Profit=Revenue-Total\ Cost\).

There are 600 trucks produced. According to the question, the first 500 trucks cost $7.00 each. Therefore, the total cost of the first 500 trucks is \(\displaystyle \$7.00\cdot 500=\$3500\).

The other 100 trucks cost $5.00 each for a cost of \(\displaystyle \$5.00\cdot 100=\$500\).

Add these together to find the cost of the 600 trucks: \(\displaystyle \$3500+\$500=\$4000\)

The total profit is easier to calculate since the selling price doesn't change: \(\displaystyle \$15.00\cdot 600=\$9000\)

At this point we have both revenue and total cost, so the answer for gross profit is \(\displaystyle \$9000-\$4000=\$5000\).

To find the average, multiply each expected profit or loss by its probability:

\(\displaystyle \dpi{100} \small average = \frac{1}{3}\times (-1000)+\frac{1}{3}\times 0 + \frac{1}{6}\times 500 + \frac{1}{6}\times 1000 \approx -\$ 83\)

To calculate profit, we find the total revenue and subtract the total expense.

The total revenue is the amount of money made from selling 388 shirts: \(\displaystyle 388\ shirts \times \$13=\$5,044\)

The total expense is the amount of money spent on buying 500 shirts: \(\displaystyle 500\ shirts \times \$5=\$2,500\)

\(\displaystyle profit=\$5,044-\$2,500=\$2,544\)

Break even profit is \(\displaystyle 0\). Plug this value into the equation to solve for the number of units:

\(\displaystyle P(x)=500x-10,000\)

\(\displaystyle 0=500x-10,000\)

\(\displaystyle 10,000=500x\)

\(\displaystyle x=\frac{10,000}{500}\)

\(\displaystyle x=20\)

Calculate the net profit by subtracting the cost of the cars from the gross profit:

\(\displaystyle \textup{net profit}=\$126,000-(\$5,000\times 4)-(\$7,000\times 8)\)

\(\displaystyle \textup{net profit}=\$126,000-\$20,000-\$56,000\)

\(\displaystyle \textup{net profit}=\$50,000\)

We need to turn the word problem into a mathematical equation, and solve.

The basic profit equation is:

\(\displaystyle G=R-(F+V)\)

Where G = gross profit, R = revenue, F = fixed or operating costs, and V = variable or production costs.

We know that we want our gross profit to be $25,000, so \(\displaystyle G=25000\).

Now, R is revenue, the money that the company earns by selling its product.  The company earns $0.35 for every widget sold, so \(\displaystyle R=0.35w\), where w = number of widgets sold.

F is the operating cost, which is $15,000.

\(\displaystyle F=15000\)

V is the cost of producing the widgets, which is $0.25 per widget.

\(\displaystyle V=0.25w\)

Plugging in our variables, we get:

\(\displaystyle 25000=0.35w-15000-0.25w\)

\(\displaystyle 40000=0.35w-0.25w\)

\(\displaystyle \frac{40000}{0.1}=w\)

\(\displaystyle w=400000\)

The company would have to sell 400,000 widgets to make a profit of $25,000

Each cookie costs 45 cents, or $0.45, to make, so the price of the ingredients will be $0.45 times the number of cookies, or \(\displaystyle 0.45 x\). 

The other expense is a flat price of the rental of the equipment, $400. 

Add the expressions to get the cost function

\(\displaystyle C(x) = 0.45x + 400\)