Based on 3.8 problem 7: Eli Daisy uses chemicals 1 and 2 to produce two drugs.Drug 1 must be at least 70% chemical 1, and Drug 2 must be at least 60% chemical 2.Up to 112 oz of Drug 1 can be sold at $8 per oz; up to 84 oz of Drug 2 can be sold at $6per oz.Up to 126 oz of chemical 1 can be purchased at $5 per oz, and up to 110 oz of chemical2 can be purchased at $4 per oz.Formulate an LP that can be used to maximize profits.Suggestion for one decision variable: x12 for oz of Chem1 in Drug 2What is the (value of the) optimal profit? z =How much of Drug 1 will be produced?How much of Chemical 2 will be purchased?

Decision Variables: Suppose-x11 be the ounces of chemical 1 in drug 1x12 be the ounces of chemical 1…

Answered: Based on 3.8 problem 7: Eli Daisy uses…

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter6: Optimization Models With Integer Variables

Section: Chapter Questions

Problem 43P

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Ali makes his living buying and selling corn. On January 1, he has 50 tons of corn and 1000 TL. On the first day of each month Ali can buy corn at the following prices per ton. January: 300 TL, February: 350 TL, March: 400 TL, April: 500 TL. On the last day of each month Ali can sell corn at the following prices per ton: January: 250 TL, February: 400 TL, March: 350 TL, April: 550 TL. Ali stores his corn in a warehouse that can hold at most 1100 tons of corn. He must be able to pay cash for all corn at the time of purchase.a) Use linear programming to model how Ali can maximize his cash on hand at the end of April.
1. The Crumb and Custard Bakery makes coffee cakes and Danish pastries in large pans. The main ingredients are flour and sugar. There are 25 pounds of flour and 16 pounds of sugar available, and the demand for coffee cakes is 5. Five pounds of flour and 2 pounds of sugar are required to make a pan of coffee cakes, and 5 pounds of flour and 4 pounds of sugar are required to make a pan of Danish. A pan of coffee cakes has a profit of $1, and a pan of Danish has a profit of $5. Determine the number of pans of cakes and Danish to produce each day so that profit will be maximized. REQUIRED: A. Formulate a linear programming model for this problem. B. Solve this model by using graphical analysis. C. How much flour and sugar will be left unused if the optimal numbers of cakes and Danish are baked?
Mete makes his living buying and selling corn. On January 1, he has 50 tons of corn and 1000 TL. On the first day of each month Mete can buy corn at the following prices per ton. January: 300 TL, February: 350 TL, March: 400 TL, April: 500 TL. On the last day of each month Mete can sell corn at the following prices per ton: January: 250 TL, February: 400 TL, March: 350 TL, April: 550 TL. Mete stores his corn in a warehouse that can hold at most 1100 tons of corn. He must be able to pay cash for all corn at the time of purchase. How Mete can maximize his cash on hand at the end of April. Which of the following is the correct objective function for the given statement? Please use (Xi = Tons of corn purchased at the beginning of month i.; Yi = Tons of corn sold at the end of month i.)
1. Compare the LP relaxations of the three integer optimization problems: (Problem 1) max 14*x1 + 8*x2 + 6*x3 + 6*x4s.t. 28*x1 + 15*x2 + 13*x3 + 12*x4 <= 39x1, x2, x3, x4 \in {0,1} (Problem 2) max 14*x1 + 8*x2 + 6*x3 + 6*x4s.t. 2*x1 + x2 + x3 + x4 <= 2x1, x2, x3, x4 \in {0,1} (Problem 3) max 14*x1 + 8*x2 + 6*x3 + 6*x4s.t. x2 + x3 + x4 <= 2x1 + x2 <= 1x1 + x3 <= 1x1 + x4 <= 1x1, x2, x3, x4 \in {0,1} Among these three problems, the LP relaxation of which problem can offer a solution whose objective value is closer to the optimal value of the corresponding integer optimization? Problem 2 Problem 3 Problem 1
This exercise is based on the following data on four bodybuilding supplements. (Figures shown correspond to a single serving.) Creatine(grams) L-Glutamine(grams) BCAAs(grams) Cost($) Xtend(SciVation) 0 2.5 7 1.00 Gainz(MP Hardcore) 2 3 6 1.10 Strongevity(Bill Phillips) 2.5 1 0 1.20 Muscle Physique(EAS) 2 2 0 1.00 Your personal trainer suggests that you supplement with at least 10 grams of creatine, 42 grams of L-glutamine, and 96 grams of BCAAs each week. You are thinking of combining Xtend and Gainz to provide you with the required nutrients. How many servings of each should you combine to obtain a week's supply that meets your trainer's specifications at the least cost? (If an answer does not exist, enter DNE.) servings of xtends = ervings of gainz =
Problem There are three factories on the Momiss River. Each emits two types of pollutants, labeled P1 and P2, into the river. If the waste from each factory is processed, the pollution in the river can be reduced. It costs $1500 to process a ton of factory 1 waste, and each ton processed reduces the amount of P1 by 0.10 ton and the amount of P2 by 0.45 ton. It costs $1000 to process a ton of factory 2 waste, and each ton processed reduces the amount of P1 by 0.20 ton and the amount of P2 by 0.25 ton. It costs $2000 to process a ton of factory 3 waste, and each ton processed reduces the amount of P1 by 0.40 ton and the amount of P2 by 0.30 ton. The state wants to reduce the amount of P 1in the river by at least 30 tons and the amount of P2 by at least 40 tons. Use Solver to determine how to minimize the cost of reducing pollution by the desired amounts. Use SolverTable to investigate the effects of increases in the minimal reductions required by the state. Specifically, see what…
BIG produces four types of yogurts A, B, C, and D. Each box of yogurt carries protein, sugar, and Fat. The following table provides information about content of each box of yogurt together with production cost of each box. Protein /Box Sugar/Box Fat/Box Production Cost/Box Yogurt A 10 3 1.5 $ 2.00 Yogurt B 20 2 1 $ 3.00 Yogurt C 30 2.5 1.5 $ 5.00 Yogurt D 20 2 1.5 $ 3.50 BIG wants to produce yogurts in such a way that will provide at least 400 grams of protein with minimum production cost. However, BIG also have to make sure they are not providing more than 200 gm of Sugar and 200 gm of Fat while providing the required protein. Moreover, BIG has to produce at least one unit of each type of yogurt and the number of yogurt A produced should not be more than the number of yogurt C produced. SOLVE USING EXCEL SOLVER
A beer company has divided Bloomington into two territories. If the company spends x1 dollars on promotion in territory 1, it can sell 60x11/2 cases of beer there; and if it spends x2 dollars on promotionin territory 2, it can sell 40x2 1/2 cases of beer there. Each case of beer sold in territory 1 sells for $10 and incurs $5 in shipping and production costs. Each case of beer sold in territory 2 sells for $9 and incurs$4 in shipping and production costs. A total of $5000 is available for promotion.a. How can the company maximize its profit?b. If an extra dollar could be spent on promotion, by approximately how much would the company’s profit increase? By how much would its revenue increase?c. Use SolverTable to see how a change in the price of beer 1 affects the optimal solution. Do the samefor a change in the price of beer 2.
I NEED HELP WITH QUESTION D AND E. Adirondack Savings Bank (ASB) has $1,000,000 in new funds that must be allocated to home loans, personal loans, and automobile loans. The annual rates of return for the three types of loans are 7% for home loans, 12% for personal loans, and 9% for automobile loans. The bank's planning committee has decided that at least 40% of the new funds must be allocated to home loans. In addition, the planning committee has specified that the amount allocated to personal loans cannot exceed 60% of the amount allocated to automobile loans. a. Formulate a linear programming model that can be used to determine the amount of funds ASB should allocate to each type of loan in order to maximize the total annual return for the new funds. b. How much should be allocated to each type of loan? What is the total annual return? What is the annual percentage return? c. If the interest rate on home loans increased to 9%, would the amount allocated to each type of loan…
Adirondack Savings Bank (ASB) has $1,000,000 in new funds that must be allocated to home loans, personal loans, and automobile loans. The annual rates of return for the three types of loans are 7% for home loans, 12% for personal loans, and 9% for automobile loans. The bank's planning committee has decided that at least 40% of the new funds must be allocated to home loans. In addition, the planning committee has specified that the amount allocated to personal loans cannot exceed 60% of the amount allocated to automobile loans. a. Formulate a linear programming model that can be used to determine the amount of funds ASB should allocate to each type of loan in order to maximize the total annual return for the new funds. b. How much should be allocated to each type of loan? What is the total annual return? What is the annual percentage return? c. If the interest rate on home loans increased to 9%, would the amount allocated to each type of loan change? Explain. d. Suppose the total amount…
The Pine Valley Board of Education must hire teachers for the coming school year. The types of teachersand the salaries that must be paid are as follows:Teacher can teach Number applying Annual salaryHistory, science 20 $21, 000History, math 15 $22, 000English, science 12 $23, 000English, math 14 $24, 000English, history 13 $25, 000Science, math 12 $26, 000For example, 20 teachers who are qualified to teach history and science have applied for jobs, and eachof these teachers must be paid an annual salary of $21, 000. Each teacher who is hired teaches the twosubjects he or she is qualified to teach. Pine Valley needs to hire 35 teachers qualified to teach history,30 teachers qualified to teach science, 40 teachers qualified to teach math, and 32 teachers qualified toteach English. The board has $1.4 million to spend on teachers’ salaries. A penalty cost of $1 is incurredfor each dollar the board goes over budget. For each teacher by which Pine Valley’s goals are unmet,the following…
A dietitian wishes to plan a meal around three foods. The percentages of the daily requirements of proteins, 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 6 8 Carbohydrates (%) 10 12 6 Iron (%) 5 4 12 The dietitian desires each meal to meet exactly the daily requirement of proteins, carbohydrates, and iron (100%) of each.(i) Using the information in the table above, write a system of three equations.(ii) Write the system in matrix form Ax= b .(iii) Using the Inverse Method, determine how many ounces of each food should the dietitian include in the meal to meet the daily requirements exactly

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