A factory makes A factory makes two types of lock, standard and large. The maximum number of standard locks that the factory can make is 100. The maximum number of large locks that the factory can make is 80. The factory must make at least 60 locks in total. The factory must make more large locks than standard locks. Each standard lock requires 2 screws, and each large lock requires 8 screws, and the factory must use a least 320 screws. A standard lock costs 21 Pounds to make and a large lock costs 43 to make. The factory manager wishes to minimize the total daily production cost of the locks. Formulate the linear programming model.

A population gathers plants and animals for survival. They need at least 440 units f energy, 300 units of protein, and 8 hides. One unit of plants provides 30 units of energy, 10 units of protein, and 0 hides. One animal provides 20 units of energy, 25 units of protein, and 1 hide. Only 26 units of plants and 27 animals are available. It costs 20 hours of labor to gather one unit of a plant and 12 hours for an animal. Find how many units of plants and animals should be gathered to meet the requirements with a minimum number of hours of labor. The population should gather 3 units of plants and 11 animals. (Simplify your answers.)

Ruff, Inc. makes dog food out of chicken and grain. Chicken has 10 grams of protein and 5 grams of fat per ounce, and grain has 2 grams of protein and 2 grams of fat per ounce. A bag of dog food must contain at least 208 grams of protein and at least 178 grams of fat. If chicken costs 11¢ per ounce and grain costs 1¢ per ounce, how many ounces of each should Ruff use in each bag of dog food to minimize cost?

A company produces three types of bookcases: Standard, Deluxe, and Premium. Each bookcase must be sanded, assembled and painted. The Standard model requires 1 hour to sand, 2 hours to assemble, and 1 hour to paint. The Deluxe model requires 2 hours to sand, 3 hours to assemble and 1 hour to paint. The Premium model requires 1 hour to sand, 4 hours to assemble and 2 hours to paint. There are 170 hours available for sanding, 320 hours for assembling and 130 hours for painting. How many of each product can be made? Solve using cramers rule. a. wriite the system of equations for this information. identify variables  b. write and label each of the four determinants, do not evaluate. c. solve for only the first variable in the system. use co-factors and minors to solve the d determinant. label the answer

An application runs two different types of advertisements, "long ads" and "short ads". A long ad costs a company 25 cents each time it is run and a short ad costs a company 17 cents each time it is run. If an advertiser ran a total of 492 long and short ads and it cost them $107.64, how many long ads did they run?

Ruff, Inc. makes dog food out of chicken and grain. Chicken has 10 grams of protein and 5 grams of fat per ounce, and grain has 2 grams of protein and 2 grams of fat per ounce. A bag of dog food must contain at least 238 grams of protein and at least 158 grams of fat. If chicken costs 9¢ per ounce and grain costs 1¢ per ounce, how many ounces of each should Ruff use in each bag of dog food to minimize cost?  grain ___oz chicken ____oz

Cholesterol intake should be limited to 300 milligrams or less each day. Two McDonald's Quarter Pounders and three Burger King Whoppers with cheese contain 520 milligrams of cholesterol. Three Quarter Pounders and one Whopper  with exceed the suggested daily intake by 53 milligrams. Determine the cholesterol content in each item.

The U-Drive Rent-A-Truck company plans to spend $8 million on 280 new vehicles. Each commercial van will cost $25,000, each small truck $30,000, and each large truck $40,000. Past experience shows that they need twice as many vans as small trucks. How many of each type of vehicle can they buy? They can buy vans, small trucks, and large trucks.

A diet is to contain at least 1596 units of carbohydrates, 2700 units of proteins, and 2568 calories. Two foods are available: F₁ which costs $0.02 per unit and F2, which costs $0.04 per unit. A unit of food F₁ contains 2 units of carbohydrates, 5 units of proteins and 6 calories. A unit of food F₂ contains 8 units of carbohydrates, 5 units of proteins and 4 calories. Find the minimum cost for a diet that consists of a mixture of these two foods and also meets the minimal nutrition requirements. Corner points of the feasible region: If there is more than one corner point, type the points separated by a comma (i.e. (1,2),(3,4)). Minimum cost is: $ when F₁ = and F2 = units units.