Cheen Corporation makes two products that are processed in two machines. The objective function and the constraints are as follows: Max P = 16A + 8B 8A + 12B ≤ 72 8A + 4B ≤ 40 A ≥ 0; B ≥ 0 where A is the number of units of the first product. B is the number of units of the second product. What is the maximum possible profit?

Cheen Corporation makes two products that are processed in two machines. The objective function and the constraints are as follows: Max P = 16A + 8B 8A + 12B ≤ 72 8A + 4B ≤ 40 A ≥ 0; B ≥ 0 where A is the number of units of the first product. B is the number of units of the second product. What is the maximum possible profit?

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 56P

See similar textbooks

Similar questions

What is the objective function and constraints? A fruit juice company makes two special drinks by blending apple and pineapple juices. The first drink uses 30% apple juice and 70% pineapple, while the second drink uses 60% apple and 40% pineapple. There are 1000 liters of apple and 1500 liters of pineapple juice available. If the profit for the first drink is P60 per liter and that for the second drink is P50, Formulate an LP that will find the number of liters of each drink that should be produced in order to maximize the profit.
Set up the objective function and the constraints, but do not solve.Chemical Products makes two insect repellents, Regular and Super. The chemical used for Regular is 15% DEET, and the chemical used for Super is 25% DEET. Each carton of repellent contains 24 ounces of the chemical. In order to justify starting production, the company must produce at least 14,000 cartons of insect repellent, and it must produce at least twice as many cartons of Regular as of Super. Labor costs are $9 per carton for Regular and $4 per carton for Super. How many cartons of each repellent should be produced to minimize labor costs if 70,680 ounces of DEET are available? (Let x represent the number of cartons of Regular, y the number of cartons of Super, and z the labor costs in dollars.) z = , subject to total production ratio of carton type amount of DEET x ≥ 0, y ≥ 0
Given this linear programming model, solve the model and then answer the questions that follow. Maximize Z = 12x1 + 18x2 + 15x3 where x1 = the quantity of product 1 to make, etc. Subject to Machine: 5x 1 + 4x 2 + 3x 3 ≤ 160 minutes Labor: 4x1 + 10x2 + 4x3 ≤ 288 hours Materials: 2x 1 + 2x2 + 4x3 ≤ 200 pounds Product 2: x2 ≤ 16 units x1, x2, x3 ≥ 0 a) Are any constraints binding? If so, which one(s)? b) If the profit on product 3 were changed to $22 a unit, what would the values of the decision variables be? The objective function? Explain. c) If the profit on product 1 were changed to $22 a unit, what would the values of the decision variables be? The objective function? Explain. d) If 10 hours less of labor time were available, what would the values of the decision variables be? The objective function? Explain. e) If the manager decided that as many as 20 units of product 2 could be produced (instead of 16), how much additional profit would be generated? f) If profit per unit on each…
The Tycron Company produces three electrical products—clocks, radios, and toasters. These products have the fol-lowing resource requirements:The manufacturer has a daily production budget of $2000and a maximum of 660 hours of labor. Maximum dailycustomer demand is for 200 clocks, 300 radios, and 150toasters. Clocks sell for $15, radios, for $20, and toasters,for $12. The company desires to know the optimal productmix that will maximize profit.Formulate and solve a linear programming model forthis problem. Resource RequirementsProduct Cost/Unit Labor Hours/UnitClock $ 7 2Radio 10 3Toaster 5 2
A decision problem has the following three constraints: 70X + 6Y <= 420; 24X + 3Y= 72; and 11X - Y <= 14 . The objective function is Min 17X + 38Y . The objective function value is : a. 338 b. 676 c. unbounded d. infeasible e. 0
Given this linear programming model, solve the model and then answer the questions that follow.Maximize Z = 12x1 + 18x2 + 15x3 where x1 = the quantity of product 1 to make, etc.Subject toMachine 5x1 + 4x2 + 3x3 ≤ 160 minutes Labor 4x1 + 10x2 + 4x3 ≤ 288 hoursMaterials 2x1 + 2x2 + 4x3 ≤ 200 poundsProduct 2 x2 ≤ 16 units x1, x2, x3 ≥ 0 a. Are any constraints binding? If so, which one(s)?
How will a change in the right-hand-side value for a constraint affect the optimalsolution?
Use Linear Programming. 2. In a grocery store, shelf space is limited and must be used effectively to increase profit. Two cereal items, FL and KC, compete for total shelf space of 60 square feet. A box of FL occupies 0.2 ft2 and a box of KC needs 0.4 ft2. The maximum daily demands of FL and KC are 200 and 120 boxes, respectively. A box of FL nets PhP 10 in profit and a box of KC PhP 13.50. The owner of the grocery thinks that because the unit profit of KC is 35% higher than that of FL, KC should also be allocated 35% more space than FL, which amounts to allocating about 57% to KC and 43% to FL. What do you think?
what is the dual equivalent and the final tableau of the given primal linear programming model?Min Y₀ = 10Y₁ + 8Y₂s.t.Y₁ + 2Y₂ ≥ 52Y₁ - Y₂ ≥ 12Y₁ + 3Y₂ ≥ 4Y₁ ≥ 0, Y₂ is unrestrictedprove or disprove the complementary slackness theorem.
Use Sensitivity Information. If the right hand side of constraint 1 increases by 9 units, what answer characterizes the impact on the optimal solution?
What is Optimization? How many methods are there to calculate it? Explain this? 2- What do we mean by function Objective? What do we mean by constraints? 3- Give three practical examples (physical or engineering) of a target function with a constraint
Find the indicated maximum or minimum value of the objective function in the linear programming problem. Minimize g = 10x + 6y subject to the following. x + 2y ≥ 10 2x + y ≥ 11 x + y ≥ 9 x ≥ 0, y ≥ 0