A clothing business finds there is a linear relationship between the number of shirts,nn,it can sell and the price,pp, it can charge per shirt. In particular, historical data shows that 30003000 shirts can be sold at a price of $122, while 1300013000 shirts can be sold at a price of $52. Give a linear equation in the form p=mn+bp=mn+b that gives the price pp they can charge for nn shirts.

Answer: p=p=1250x+0 syntax error. Check your variables - you might be using an incorrect one.

Round the value of your slope to three decimal places. Be careful to use the proper variable and use the Preview button to check your syntax before you submit your answer.

Question 2

Your firm is considering adding a product line. The accounting department has determined that the cost function for this new product will be C(x)=40x+3000C(x)=40x+3000 and the revenue function will be R(x)=60xR(x)=60x, where xx is the number of units sold. Additionally, the sales department has determined that you reasonably can expect to sell around 155155 units. You must decide whether to go ahead with the new product line. Find the break-even quantity: Find the profit function: P(x)=P(x)= Make your decision:

• Cancel the product line: the quantity needed to break even is more than our firm can reasonably expect to sell.
• Proceed with the product line: the products are profitable and we can reasonably expect to meet our break-even quantity.
• Cancel the product line: producing these products is not profitable.

Question 3

A company produces two types of drills, a corded and cordless. The cord-type drill requires 2 hours to make, and the cordless model requires 4 hours. The company has 480 work hours per day for manufacturing and daily storage of 160 drills per day. Let xx = the number of cordless drills produced per day and yy = the number of corded drills produced per day. Write the system of inequalities 480480 160160 Graph the system of inequalities.

Question 4

The Pear company sells pPhones. The cost to manufacture xx pPhones is C(x)=30x2+61000x+19909C(x)=-30x2+61000x+19909dollars (this includes overhead costs and production costs for each pPhone). If the company sells xx pPhones for the maximum price they can fetch, the revenue function will be R(x)=34x2+189000xR(x)=-34x2+189000x dollars. How many pPhones should the Pear company produce and sell to maximimze profit? (Remember that profit=revenue-cost.)

Question 5

The value of China's exports of automobiles and parts (in billions of dollars) is approximately f(x)=1.8208e0.3387xf(x)=1.8208e0.3387x, where x = 0 corresponds to 1998. In what year did/will the exports reach $7.7 billion?