BSTA 450 - Review Sheet - Test 2 1. Consider the following linear programming problem: Maximize Z = 400 x + 100y Subject to 8 x + 10y ≤ 80 2 x + 6y ≤ 36 x≤ 6 x, y ≥ 0 BSTA 450 Find the optimal solution using the graphical method (use graph paper). Identify the feasible region and the optimal solution on the graph. How much is the maximum profit? Consider the following linear programming problem: Minimize Z = 3 x + 5 y (cost, $) subject to 10 x + 2 y ≥ 20 6 x + 6 y ≥ 36 y ≥ 2 x, y ≥ 0 Find the optimal solution using the graphical method (use graph paper). Identify the feasible region and the optimal solution on the graph. How much is the minimum cost? 2. The Turner-Laberge Brokerage firm has just been instructed by one of its clients …show more content…
Each ingredient contains the same three antibiotics in different proportions. One gram of ingredient 1 contributes 3 units, and ingredient 2 contributes 1 unit of antibiotic 1; the drug requires 6 units. At least 4 units of antibiotic 2 are required, and the ingredients each contribute 1 unit per gram. At least 12 units of antibiotic 3 are required; a gram of ingredient 1 contributes 2 units, and a gram of ingredient 2 contributes 6 units. The cost for a gram of ingredient 1 is $80, and the cost for a gram of ingredient 2 is $50. The company wants to formulate a linear programming model to determine the number of grams of each ingredient that must go into the drug in order to meet the antibiotic requirements at the minimum cost. Formulate a linear programming model for this problem. Consider the following linear programming problem: Maximize Z = 300 x1 + 500 x2 7. subject to : 3x1 + 5 x2 ≤ 30 x1 + x2 ≥ 18 x1 , x2 ≥ 0 Why this problem has no solution? Definitions and concepts to know 1. 2. 3. 4. 5. 6. 7. 8. 9. Decision variable Objective function Constraint Feasible region Isoprofit line Isocost line Unboundedness Infeasibility Maximization problem 10. Minimization problem 11. Redundant constraint 12. Alternate optimal solutions 13. Binding constraint 14. Slack value 15. Corner point method 16. Classical problems: a. the marketing problem b. the investment problem c. the blend problem d. the product mix problem e. the transportation
I found the solution to the Woo’s problem by using the tools I mentioned above. I converted the problems constraints into inequalities and from there I was able to put all of them onto a graph and find the feasible region. Then from the prices given in the problem I was able to make my first profit line, and was able to find out the
c. Explain how the location of each curve graphed in question 7b would be altered if (1) total fixed cost had been $100
(3 marks) c) Determine the optimal number of bus and train travelers. (2 marks) d) Say a train strike significantly reduced the number of trains available. By how much would the train capacity constraint have to fall for the optimal solution to be altered? (2 marks)
* Use the profit maximization rule MR = MC to determine your optimal price and optimal output level now that you have market power. Compare these values with the values you generated in Assignment 1. Determine whether your price higher is or lower.)
How We Chose Our Topic:As our point, we picked Toussaint Louverture. We picked this theme by looking through the saple point list and chose an !ew that spoke to our interests. We as a whole concurred that Toussaint and his administration amid the Haitian "advancement was a fitting decision since it was a subject that we didn't know anything about. Additionally, the sub#ect was one that was ore uncoon, not at all like any different subjects on the rundown. The exact opposite thing that persuaded us to coplete our pro#ect on Toussaint Louverture was that he drove the main success!ul slave defiance
14) Consider the following transshipment problem. The shipping cost per unit between nodes 1 and 2 is $10, while the shipping cost per unit between nodes 2 and 3 is $12. What is the objective function?
30. The manager of the local National Video Store sells videocassette recorders at discount prices. If the store does not have a video recorder in stock when a customer wants to buy one, it will lose the sale because the customer will purchase a recorder from one of the many local competitors. The problem is that the cost of renting warehouse space to keep enough recorders in inventory to meet all demand is excessively high. The manager has determined that if 90% of customer demand for recorders can be met, then the combined cost of lost sales and inventory will be minimized. The manager has estimated that monthly demand for recorders is normally distributed, with a mean of 180 recorders and a standard deviation of 60. Determine the number of recorders the manager should order each month to meet 90% of customer demand.
Religion is what some people use to get through everyday challenges. People pray or read their Bible to make them feel safe or perhaps even to call on something bigger than themselves to help them out in times of need. Also for the people who do believe in God, God is their strength to keep going and to never give up. His stories are always there to brighten their mood, this is what El-ahrairah and Frith are for the rabbits in “Watership down”. Frith and El- ahrairah are what God is for the people who believe in him, Frith is the one who made the world and he is the one they call on when they need help and in a lot of ways he relates to the christian version of God.
As Freire mentioned the idea that banking is basically education, as in teachers are “depositing” information into the minds and ideas of their students. I believe that the act of authentic liberation is a “withdrawal” from a student’s bank account. In order for a student to make a withdrawal from their account, the student must first be aware of the balance in their account. Being aware of one’s balance is what I see as being aware of one’s incompleteness. Once aware of the balance, only then can a student make a “withdrawal” from a student’s account. My question is, how can a student be aware of their balance if the only person who can see their balance is the person making deposits? I am still rather confused on how a teacher, or those who
Max is required to spend more than 300 minutes to complete assignments, and he can use at most 20 paper sheets. Let's form a system of inequalities to represent Max's conditions. Let W denote the number of writing assignments he completes and M the number of math assignments he
Irwin Textile Mills produces two types of cotton cloth denim and corduroy. Corduroy is a heavier grade of cotton cloth and, as such, requires 8 pounds of raw cotton per yard, whereas denim requires 6 pounds of raw cotton per yard. A yard of corduroy requires 4 hours of processing time; a yard od denim requires 3.0 hours. Although the demand for denim is practically unlimited, the maximum demand for corduroy is 510 yards per month. The manufacturer has 6,500 pounds of cotton and 3,000 hours of processing time available each month. The manufacturer makes a profit of $2.5 per yards of denim and $3.25 per yard of corduroy. The manufacturer wants to know how many yards of each type of cloth to produce to maximize profit. Formulate the model and put into standard form. Solve it
Problem #2.” (To make your life easier, optimal stocking quantity, Q, is computed by the
The next thing that I need to do is to solve for the two following scenarios. “The Burbank Buy More store is going to make an order which will include at most 60 refrigerators. What is the maximum number of TVs which could also be delivered on the same 18-wheeler? Describe the restrictions this would add to the existing graph”.
(0.94,0) 0.85(0.94) + 0.65(0) = $0.799 3) Linear Programing Model Decision Variables: Let a = Automobile Loans Let f = Furniture Loans Let o = Other Secured Loans Let s = Signature Loans Let r = Risk-free Securities Objective Function: Maximize Z = 0.8a + 0.1f + 0.11o + 0.12s + 0.9r where Z =
Products supply are mainly based on customer demand which changes for each individual product at individual location. This makes to forecast and optimization a difficult task where estimating demand and ordering goods is not desirable even if it is possible. In order to manage inventory, optimize return of investments solution which can optimize Supply chain demand and planning is needed.