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Moore’s Meatpacking Company producesahot dog mixture in 1000- pound batches. The mixturecontains two ingredients- chicken and beef.The cost per pound of each of these ingredients is asfollows:
IngredientCost/lb.
Chicken 3
Beef 5
Each batch has the following recipe requirements:
1.At least 500 pounds of chicken
2.At least 200 pounds of beef
The ratio of chicken to beef must be at least 2 to 1.
1) The company wants to know the optimalmixture of ingredientsthatwillminimizecost.
2)Formulatea linear programming model for this problem.
A farmer is preparing to plant a crop in the spring and needs to fertilize a field. There are twobrands of fertilizer to choose from, Super-Gro and Crop Quick. Each brand yields a specific amountof Nitrogen and Phosphate per bag as follows.
Brand Chemical Contribution
Nitrogen (lb/bag) Phosphate (lb/bag)
Super-Gro 24
Crop Quick 43
The farmer’s field requires at least 16 pounds of nitrogen and at least 24 pounds of phosphate. Super- gro costs M6 per bag, and Crop Quick costs M3per bag.
1) The farmer wants to know how many bags of each brand to purchase in order to minimize thetotal cost of fertilizing.
2) Formulate a mathematical model of the problem.
A management consultant firm employs 50 highly competent people of which 20 are male
and 30 are female. A committee of 10 members from all 50 employees is chosen at random.
The probability that all the committee members are of the same gender (i.e. either all male or
all female) is (to 6 decimal places):
A retail store stocks two types of shirts A and B. These are packed in attractive card boxes.During a week the store can sell a maximum of 400 shirts of type A and a maximum of 300 shirts oftype B. The storage capacity, however, is limited to a maximum of 600 of both types combined. TypeA fetches a profit of M2 per unit and Type B a profit of M5 per unit.
How many of each type thestore should stock per week to maximize the total profit? Formulate a mathematical model of theproblem.
Roma grower has a 50-acre farm on which to plant cabbages and tomatoes. The grower has available 300 hours of labourper week and 800 tons of fertilizer, and he has contracted shipping space for a maximum of 26 acre’s worth of cabbages and 37 acres’
worth of tomatoes. An acre of cabbages requires 10 hours of labour and 8 tons of fertilizer,whereas an acre of tomatoes requires 3 hours of labour and 20 tons of fertilizer.
The profit from an acre of cabbages is M400, and the profit from an acre of tomatoes is M300. Thefarmer wants to know the number of acres of cabbages and tomatoes to plant to maximize profit.
Formulate this as a linear programming
problem.
Paul Fertilizer Company makes a fertilizer using two chemicals that provide nitrogen, Phosphate,and potassium. A pound of ingredient 1 contributes 10 ounces of nitrogen and 6 ounces of phosphate,while a pound of ingredient 2 contributes 2 ounces of nitrogen, 6 ounces of phosphate, and 1 ounceof potassium. Ingredient 1 cost M3 per pound, and ingredient 2 costs M5 per pound. The companywants to know to know how many pounds of each chemical ingredient to put into a bag of fertilizerto meet the minimum requirements of 20 ounces of nitrogen, 36 ounces of phosphate, and two ouncesof potassium while minimizing the cost.
•Formulate a linear programming model for this problem
After graduating with a BCom degree, Tim had interviews with two companies A and B
Suppose that there is a 20% chance that he will be offered the job by company A and a 15%
chance that he will be offered a job with company B. Suppose that each company is unaware
that he has had an interview with the other company. What is the probability that he will be
offered a job by exactly one of the companies? (answer to 2 decimal places):
A box contains three two-sided coins of the same size and weight. Coin A is a standard
unbiased coin, while Coin B has two heads. Coin C is biased so that a tail is twice as likely to
occur as the head. A coin is randomly selected from the box, tossed and landed on "heads"
What is the probability that it is Coin C?
Five accounts are randomly sampled without replacement from a box of forty accounts. The
box contains thirty accounts that have a debit balance. What is the probability of selecting at
least one account with a credit balance?
A large manufacturing company is in the process of training its personnel in quality-control
procedures. At present 40% of the assembly lines use control charts, 40% use inspection
techniques and the remaining assembly lines do not use any method for controlling quality.
Assume that an assembly line can only use a maximum of 1 method, if any, for quality
control.
The assembly lines that use control charts have a 1% defective rate. The assembly lines
that use inspection techniques have a 5% defective rate. The assembly lines that do not use
any quality-control techniques have a 12% defective rate. The probability that an item
produced by this company is defective is (correct to 3 decimal places):
#340153 on Dec 2023