The maximum production of a soft-drink bottling company is 5000 cartons per day. The company produces two kinds of soft drinks, regular and diet. It costs $1.00 to produce each carton of regular and$1.20 to produce each carton of diet. The daily operating budget is $5400. The profit is$0.15 per carton on regular and $0.17 per carton on diet drinks. How much of each type of drink is produced to obtain the maximum profit?

A manufacturer produces custom steel products from recycled steel in which each ton of the product must contain 4 pounds of chromium, 8 pounds of tungsten, and 7 pounds of carbon. The manufacturer has three sources of recycled steel: Source l: Each ton contains 2 pounds of chromium, 8 pounds of tungsten, and 6 pounds of carbon. Source 2: Each ton contains 3 pounds of chromium, 9 pounds of tungsten, and 6 pounds of carbon. Source 3: Each ton contains 12 pounds of chromium, 6 pounds of tungsten, and 12 pounds of carbon. Let x, y, and z denote the percentages of the first, second, and third recycled steel sources that will be melted down for one ton of the product. Find (but do not solve) a linear system in x, y, and z whose solution tells the percentage of each source that must be used to meet the requirements for the finished product.

When would it be beneficial to use exclusive distribution rather than intensive distribution?

Beauty Products makes two styles of hair dryers, the Petite and the Deluxe. It requires 1 hour of labor to make the Petite and 2 hours of labor to make the Deluxe. The materials cost $4 for each Petite and$3 for each Deluxe. The profit is $5 for the Petite and$6 for the Deluxe. The company has 3950 labor-hours available each week and a materials budget of $9575 per week. How many of each dryer should be made each week to maximize profit?

For each x in [0, 1], let $f(x) = x$ if x is rational, and let $f(x) = 1- x$ if x is irrational. Prove that: (a) $f(f(x))=x$ for all x in [0, 1]. (b) $f(x)+f(1-x)=1$ for all x in [0, 1]. (c) f is continuous only at the point $x=\frac{1}{2}$. (d) f assumes every value between 0 and 1. (e) $f(x+y)-f(x)-f(y)$ is rational for all x and y in [0, 1].

Precision Machinists makes two grades of gears for industrial machinery, standard and heavy duty. The process requires two steps. Step 1 takes 8 minutes for the standard gear and 10 minutes for the heavy duty. Step 2 takes 3 minutes for the standard gear and 10 minutes for the heavy duty. The company’s labor contract requires that it use at least 200 labor-hours per week on the step 1 equipment and 140 labor-hours per week on the step 2 equipment. The materials cost $15 for each standard gear and$22 for each heavy duty. How many of each gear should be made each week to minimize costs?

The Nut Factory produces a mixture of peanuts and cashews. The company guarantees that at least 40% of the total weight is cashews. It has a contract to produce 1000 pounds or more of the mixture. The peanuts cost $0.80 per pound, and the cashews cost$1.50 per pound. Find the amount of each kind of nut the company should use to minimize the cost: (a) If 720 pounds of peanuts are available, (b) If 500 pounds of peanuts are available.

$$800 \div 16$$

Find the inverse of the matrices.

$$\left[\begin{array}{rrrr}{-3} & {-1} & {1} & {-2} \\ {-1} & {3} & {2} & {1} \\ {1} & {2} & {3} & {-1} \\ {-2} & {1} & {-1} & {-3}\end{array}\right]$$

Prove Theorem 5-6: All right angles are congruent. Given: Angle 1 and angle 2 are right angles. Prove: $\angle 1 \cong \angle 2$

find the area of the region bounded by the line y+3=x,x=1,x=5.

Suppose you plan to save $12 per week. You have already saved$7.50. In how many weeks will you have saved at least $100?

Two foods, I and II, contain the following percentages of carbohydrates, protein, and fat: $$ \begin{matrix} \text{Food} & \text{Carbohydrates} & \text{Protein} & \text{Fat}\\ \text{I} & \text{40\\%} & \text{50\\%} & \text{6\\%}\\ \text{II} & \text{60\\%} & \text{20\\%} & \text{4\\%}\\ \end{matrix} $$ Food I costs 3¢ per gram, and food II costs 4c per gram. Determine the amount of each that should be served to produce at least 10 grams of carbohydrates, 7.5 grams of protein, and 1.2 grams of fat, if cost is to be minimized.

Match (by letter) the following items with the description or example that best fits. Each letter is used only once.

$$\begin{matrix} \text{Terms}\\ \hline \text{\_\_\_\_\_ 1. Vertical analysis.}\\ \text{\_\_\_\_\_ 2. Horizontal analysis.}\\ \text{\_\_\_\_\_ 3. Liquidity.}\\ \text{\_\_\_\_\_ 4. Solvency.}\\ \text{\_\_\_\_\_ 5. Discontinued operations.}\\ \text{\_\_\_\_\_ 6. Quality of earnings.}\\ \text{\_\_\_\_\_ 7. Conservative accounting practices.}\\ \text{\_\_\_\_\_ 8. Aggressive accounting practices.}\\ \end{matrix}$$

$$\begin{matrix} \text{Descriptions}\\ \hline \text{a. A company's ability to pay its current liabilities.}\\ \text{b. Accounting choices that result in reporting lower income, lower assets, and higher liabilities.}\\ \text{c. Accounting choices that result in reporting higher income, higher assets, and lower liabilities.}\\ \text{d. The ability of reported earnings to reflect the company's true earnings as well as the}\\ \text{usefulness of reported earnings to help investors predict future earnings.}\\ \text{e. A tool to analyze trends in financial statement data for a single company over time.}\\ \text{f. The sale or disposal of a significant component of a company's operations.}\\ \text{g. A means to express each item in a financial statement as a percentage of a base amount.}\\ \text{h. A company's ability to pay its long-term liabilities.}\\ \end{matrix}$$