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1. A Cereal Company makes a cereal from several ingredients. Two of the ingredients, oats and rice, provide vitamins A and B. The company wants to know how many ounces of oats and rice it should include in each box of cereal to meet the minimum requirements of 45 milligrams of vitamin A and 13 milligrams of vitamin B while minimizing cost. An ounce of oats contributes 10 milligrams of vitamin A and 2 milligram of vitamin B, whereas an ounce of rice contributes 6 milligrams of A and 3 milligrams of B. An ounce of oats costs $0.06, and an ounce of rice costs $0.03. a. Formulate a linear programming model for this problem.
b. Solve the model by using graphical analysis. 2. A Furniture Company produces chairs and tables from two resources- labor and wood. The company has 125 hours of labor and 45 board-ft. of wood available each day. Demand for chairs is limited to 5 per day. Each chair requires 7 hours of labor and 3.5 board-ft. of wood, whereas a table requires 14 hours of labor and 7 board-ft. of wood. The profit derived from each chair is $325 and from each table, $120. The company wants to determine the number of chairs and tables to produce each day in order to maximize profit. Formulate a linear programming model for this problem. a. Formulate a linear programming model for this problem.
b. Solve the model by using graphical analysis (Do not round the answers)
c. How much labor and wood will be unused if the optimal numbers of chairs and tables are produced? 3. Kroeger supermarket sells its own brand of canned peas as well as several national brands. The store makes a profit of $0.28 per can for its own peas and a profit of $0.19 for any of the national brands. The store has 6 square feet of shelf space available for canned peas, and each can of peas takes up 9 square inches of that space. Point-of-sale records show that each week the store never sales more than half as many cans of its own brand as it does of the national brands. The store wants to know how many cans of its own brand of peas of peas and how many cans of the national brands to stock each week on the allocated shelf space in order to maximize profit. a. Formulate a linear programming model for this problem.
b. Solve the model by using graphical analysis.
Using life insurance tables, a retired man determines that the probability of living 5 more years is 0.91. He decides to take out a life insurance policy that will pay $31,000 in the event that he dies during the next 5 years. How much should he b..
lisa kane borrowed8000 on an 8 60 day note. after fifteen days lisa paid 2000 on the note. on day 45 lisa paid 1000 on
We use the Fourier expansions of certain poynomial functions to compute the sum of some useful numerical series. The formulas are quite general and give, at the end, the Fourier expansion of every polynomial function.
Permutation and combination to find number of ways
A flagpole is tilted at an angle of seven degrees from he horizontal and towards the sun. It casts a shadow of 14 meters when the angle of elevation of the sun is 43 degrees. Find the length of the flagpole.
3.Suppose thet g . odd, f°,g(x)d.3 = 2, wed g(3). = Either find f: g(g)dx, or show there is not enough informotion to .a g(3.1.3.Suppose that g is odd, R 4−2g(x) dx = 2, and R −4−6g(x) dx = 3. Either find R 62g(x) dx, or show there is notenough infor..
A study of freeway flow at a particular site has resulted in a flow-density relationship.
broussard skateboards are expected to increase by 15 from 8 million in 2013 to 9.2 million in 2014. its assets totaled
Suppose A, B ⊂ R are two bounded sets (i.e., bounded above and below).Show that A - B = {a - b|a ∈ A, b ∈ B} is also bounded, and that sup(A - B) = sup(A) - inf(B)
Find the volume of a pyramid of height 160 feet that has a square base of side 300 feet. These dimensions are half those of the pyramid in example 2.1. How does the volume compare?
The decision variables, Need a physical explanation as to why X37 = 400, X78 = 0, and X48 = 400. I need for these computer generated numbers to make sense and be able to justify them
Describe the first step to solving the power of a power compared to solving the power of a product of two factors. Give an example of solving a problem containing the power of a power.
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