6. A firm makes three different categories product: an Economy model, a standard
ID: 457050 • Letter: 6
Question
6. A firm makes three different categories product: an Economy model, a standard model and a deluxe model. Economy model contributes 63 unit to Standard model contributes 95 Rials per unit, and deluxe The omani Rials per unit. Each product category requires two materials and a manufacturing time. requirements are as follows: Material Material 2 Manufacturing Time Economy 12 Standard Deluxe For the coming period the company has 200 uints available from material 1 and 320 units of material. There is hours of manufacturing time available for the next period. How many economy model XI), standard model and Deluxe model the company should make to maximize the profit? Refer to the computer output "solver" of the problem and answer questions a to i ive Cell (Ma original Final Name Value Value SES2 16440 Variable Cells Final Reduced objective Allowable Allowable Name Value Coefficient Increase Decrease SA$2 15.5 $B$2 Constraints Final Shadow Constraint Allowable ble Name Value Side Increase Material SAS6 Material Manufacturing a. Formulate the LP model b. Fill in the blanks c. many units should be produced from each product category? What is the value of the objective function? d. Which products are basic and which are no e. If the manager wants to produce Deluxe model (Xs), what changes he should make? A new competitor entered the market providing Economy product with a competitive price, the manager decided to decrease the profit contribution of product XI by 6 rials and 500 baiza. What is the effect of the manager decision on optimal solution and on the value of objective function? g. Which islare non-binding? What is itstheir h. Would you recommend increasing the capacity of material l to 210 u Explain material 2 by how is that going to affect i. If there is a shortage of material l by 25 units and an axcess in the value of the objective function? j. the company for every unit increase in material l and 10 rials for every unit increase in material 2, would you increase material l by 10 units or material 2 by 15 units? explaiExplanation / Answer
f) The new profit on economy model - 56.5 Rials
The profit objectivev would change to
Max Profit -> 56.5x+ 95y+ 135 z
Running the solver this time,
the optimum units to produce would remain same 1.e. 80, 120, 0 on economy, standard, deluxe resp.
But max profit would decrease to 15920 Rials.
g) material 1 and material 2 are binding constraints. SLack is zero for them.
Manufacturing time is non binding constraint. Slack is 320.
h) Yes, Material 1 is a binding constraint, Increasing 1 unit of M1 will increase profit by 31 Rials. If M1 cost is less than 31 Rials, it will definitely help us by increasing profit.
i) If M1 is just 175, And M2 is 370, the units will change to 0,165,0 - Economy, Standard, Deluxe. Max profit would be 17025 Rials.
j) Profit by each unit increase in M1- 31 Rials
Cost to Increase 1 unit M1- 12 Rials
Net profit to Increase 1 unit M1- 19 Rials
For M2
Profit by each unit increase in M2- 32 Rials
Cost to Increase 1 unit M2- 10 Rials
Net profit to Increase 1 unit M2- 22 Rials
It is better to increase material 2 by 15 units.
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.