2.A dietician has to develop a special diet using two foods P and Q. Each packet (containing 30 g) of food P contains 12 units of calcium, 4 units of iron, 6 units of cholesterol and 6 units of vitamin A. Each packet of the same quantity of food Q contains 3 units of calcium, 20 units of iron, 4 units of cholesterol and 3 units of vitamin A. The diet requires at least 240 units of calcium, at least 460 units of iron and at most 300 units of cholesterol. How many packets of each food should be used to minimize the amount of vitamin A in the diet? Formulate a LPP.

A company uses 3 machines X,Y and Z for their production. The company repairs each machine every time in breaks down and keeps a record of the number of breakdowns and the cost of each repair. The records for 2016 and 2021 are shown below. 2016 2021 Machine Cost of each repair (Rands) 1000 Cost of each Number of Number of repair (Rands) 800 breakdowns breakdowns 10 14 Y 400 13 800 20 2000 6. 2400 8 The cost of repair of each machine is fixed throughout the year, time machine X broke down, it cost R800 to fix it. for example in 2016, every Adapt the formula for the Laspeyres Price Index to calculate the Laspeyres "Cost of repair" Index for 2021 using 2016 as the base year. A. 137.5 В. 138.1 C. 139.8 D. 140.0

Parent W requires one of component B and two of component C. Both B and Care run on work center 10. Setup time for B is 2 hours, and run time is 0.1 hour perpiece. For component C, setup time is 2 hours, and run time is 0.15 hour per piece. Ifthe rated capacity of the work center is 80 hours, how many Ws should be producedin a week?

Rivers in North Carolina contain small concentrations of mercury that can accumulate in fish over their lifetimes. The concentration of mercury in fish tissue can be obtained by catching fish and sending samples to a lab for analysis. A study was conducted on fish from the Waccamaw and Lumber Rivers to investigate mercury levels in tissues of largemouth bass. At several stations along each river a group of fish were caught, weighed and measured; in addition a filet from each fish was sent to a lab so that the tissue concentration of mercury could be determined. In all, 171 fish were caught at 15 different research stations along the Waccamaw and Lumber Rivers. Data from fish caught at one of these stations is shown in the followinng table: length weight 1616 47.0 48.7 1862 2855 55.7 45.2 1199 1320 44.7 1225 43.8 870 38.5 1455 45.8 1220 44.0 1033 40.4 Compute the correlation between length and weight for these fish. (Assume the correlation conditions have been satisfied and round your…

Freight Crate Inc. produces small, medium, and large shipping crates used by a variety of clients and companies. Each month, Freight Crate produces and ships it's own (empty) containers out to its distributor to be sold. Data on the shipping containers' weights and costs are given in the table below: Small Medium Large Weight (lbs per container) 20 44 80 Cost to Produce (per container) $20 $40 $100 A shipment of containers must adhere to an imposed weight limit of 9,664 lbs. Furthermore, pre- vious sales data suggest that Freight Crate should produce twice as many medium containers as large containers. The company hopes to determine the total of each type of container to produce on a monthly shipping budget of $10,300. Define x, y, and z to be the total number of small, medium, and large containers produced montly, respectively.

A large institution is preparing lunch menus containing foods A and B. The specifications for the two foods are given in the following table: Units of Units of Units of Fat Carbohydrates Protein Food per Ounce per Ounce per Ounce A 1 2 1 B 1 1 1 Each lunch must provide at least 6 units of fat per serving, no more than 7 units of protein, and at least 10 units of carbohydrates. The institution can purchase food A for $0.12 per ounce and food B for $0.08 per ounce. How many ounces of each food should a serving contain to meet the dietary requirement at the least cost?

6:01 3) A dietitian wishes to plan a meal around three foods. The percentages of the daily requirements of protein, carbohydrates, and iron contained in each ounce of the three foods are summarized in the following table: Food 1 Food 2 Food 3 Protein (%) 10 Carbohydrate (%) Iron (%) 10 12 6. 5 4. 12 Determine how many ounces of each food the dietitian should include in the meal to meet exactly the daily requirements of protein, carbohydrates, and iron (100% of each).

A nutritionist is performing an experiment on student volunteers. She wants to feed one of the volunteers a daily diet that consists of a combination of three commercial diet foods: MiniCal, LiquiFast, SlimQuick. For the experiment, it is important that the volunteer consume a total of exactly 500 of potassium, 75g of protein, and 1150 IU of vitamin D every day. The amounts of these nutrients in one ounce of eacl diet food are given in the table. How many ounces of each food should the volunteer eat every day to satisfy the nutrient requirements exactly? MiniCal (1 ounce) LiquiFast (1 ounce) SlimQuick (1 ounce) Potassium (mg) 50 75 10 Protein (g) 10 3 vitamin D (IU) 90 100 50 Solve the system algebraically or use the rref in your graphing calculator to find the amount of ounces of each food needed to satisfy the nutrient requirements.

A freshly brewed shot of espresso has three distinct components: the heart, body, and crema. The separation of these three components typically lasts only 10 to 20 seconds. To use the espresso shot in making a latte, a cappuccino, or another drink, the shot must be poured into the beverage during the separation of the heart, body, and crema. If the shot is used after the separation occurs, the drink becomes excessively bitter and acidic, ruining the final drink. Thus, a longer separation time allows the drink-maker more time to pour the shot and ensure that the beverage will meet expectations. An employee at a coffee shop hypothesized that the harder the espresso grounds were tamped down into the portafilter before brewing, the longer the separation time would be. An experiment using 24 observations was conducted to test this relationship. The independent variable Tamp measures the distance, in inches, between the espresso grounds and the top of the portafilter (i.e., the harder the…

An electronics company produces transistors, resistors, and computer chips. Each transistor requires 3 units of copper, 1 unit of zinc, and 2 units of glass. Each resistor requires 3, 2, and 1 units of the three materials, and each computer chip requires 2, 1, and 2 units of these materials, respectively. How many of each product can be made with the following amounts of materials? Complete parts (a) through (c) below. (a) Let x represent the number of transistors that can be made, y the number of resistors, and z the number of computer chips. Write a system of three linear equations when the amounts of available materials are 775 units of copper, 385 units of zinc, and 470 units of glass. Choose the correct answer below. A. 3x + 3y + 2z = 385 x+2y+z=775 2x+y + 2z = 470 O C. 3x + 3y + 2z = 775 x + 2y + z = 385 2x+y + 2z = 470 The company can make 6 transistors, 2 resistors, and 3 computer chips. (b) 770 units of copper, 380 units of zinc, and 490 units of glass The company can make…