A firm makes three different categories produc an Economy model, a standard mode

Question

A firm makes three different categories produc an Economy model, a standard model and a deluxe model. Economy model contributes 63 omani Rials per unit to profit, Standard model contributes 95 Omani Rials per unit, and deluxe model contribut 35 Omani Rials per un Each product category requires two materials and a manufacturing tim The requirements are as follows: Material 1 Material 2 Manufacturing Time l is Standard For the coming period the company has 200 uints available from material l and 320 units of materiala. There is 2400 hours of manufacturing time available for the next period. economy model CXI, standard model (X) and ow many Deluxe model (X, the company should make to maximize the profi Refer to the computer output "solver" of the problem and answer questions a to i obiective Cell (Max Original Final Name Value Value Obi Variable Cells Final Reduced objective Allowable Allowable Cell Name Value Coefficient Increase Decrease SAS2 SBS2 Constraints Final Shadow Constrain Allowable Allowable Name Value R. H. Side $A$5 Material 40 SAS7 Manufacturing a. Formulate the LP model b. Fill in the blanks 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 non-basic? If the manager wants to produce Deluxe model (X), what changes he should make? f A new competitor entered the market providing Economy product (X) 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 solution and on the value of objective function? manager decision on optimal g. Which constraints isare What is its h. Would you recommend increasing the capacity of material l to 210 units? Explain by 25 and axcess in material 2 by 50, how is that going to affect a shortage of material l the value of the objective function? increase in j. If it costs the company 12 rials for every unit increase in material 1 and 10 rials for every unit material 2, would you increase material l by 10 units or material 2 by 15 units? explain 7. demand for gold-filled lockets at Bargain and Housewares is 2,420 lockets a year. Manager Veronica Winters has indicated that ordering cost is $45, and that the following price schedule applies: 1 to total s to i,199 each; and i.200 or more, s.75 each. What order size will minimize cost in each of these cases (A) Carrying cost is $.18 per locket on an annual basi (B) Carrying cost is 20 percent of price on an annual basis

Explanation / Answer

Assuming the number of units as x,y,z for economy, standard and deluxe model respectively

and assuming all unit values are non negative

the LP problem would be

a) x,y,z>=0

for maximum profit 63x+ 95y+135z ->Maximum

Constraints

1x+ 1y+1z<=200

1x+2y+4z<=320

8x+12y+14z<=2400

as we have constraints of material (M1, M2) and manufacturing time.

b) Variable Cells

$C$2 - reduced cost - (-24)

Final Values for M1, M2, Manufacturing Time - 200, 320, 2080

c) Final values of 3 materials -

Economy - 80 units

Standard - 120 units

Deluxe - 0 units

Profit - 16440 Omani Rials

d) Non basic variables - x,y,z

basic variables - Profit, Material 1, Material 2, maufacturing Time

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.