Question

M3_IND4. A gear manufacturer is planning next week's production for four types of gears. Because are limited resources in the plant for production, the manufacturer can outsource the gears by there C purchasing these gears from a regional supplier. The regional supplier can supply a maximum of 400 units of each type of gear. The table below shows the exact demand for the gears, the revenue per unit, and the outsource cost per unit if the gears are purchased from the supplier. The manufacturer generates the same revenue per unit for the gears regardless of whether the gear is manufactured in their plant and then sold to their customers or outsourced from their supplier and then sold to their customers. PRODUCT GEAR TYPE GEAR A GEAR B GEAR C GEAR D Demand 650 500 450 550 $13.75 $9.20 $12.50 $9.75 $16.90 $11.00 $18.50 $11.75 Revenue Outsource Cost When the gears are manufactured in the own plant, the gears must be processed through three different departments: forming, hardening, and deburring. The table below shows the processing time (in hours) for each type of gear in the departments as well as the capacity for each department and the cost per hour for processing the gears in those departments. The cost per hour for processing the gears is provided so that you can calculate the manufacturing cost DEPARTMENT GEAR A GEAR B GEAR C GEAR D COST PROCESS CAPACITY (hrs./unit) (hrs./unit) (hrs./unit) ($/hr.) (hrs./unit) (hours) $9.50 $8.75 $7.90 Forming Hardening Deburring 0.37 0.43 0.45 0.52 500 0.30 0.25 0.31 0.40 400 0.40 0.37 0.42 0.32 400 Formulate and solve this problem in Excel to determine the production and/or outsource plan which will meet the requirements and maximize the profit. (Hint: processing costs in the second table effect only the profit for the gears that are manufactured and not the gears that are outsourced) a) How much profit does the company for all gears they make and buy in your solution (the value of the objective function)? (enter to the nearest integer) If you could add one hour of capacity to any department to increase profit adding one hour of b) capacity to which department would generate the biggest increase in profit: Forming, Hardening, or Deburring? c) Which of the following constraints have slack? (Choose all constraints with slack): Forming, Hardening, or Deburring d) In your solution, how many Gear C's should the company make? e) If the cost per hour of the hardening process increases to $12/hr. - how many Gear D's should

Answer 1

Solletion Poefit Revenue - oud lord cost -Pfg.CoHebe GSOX 13.35 +sov x 12.So +450x16.90+ 550 Y 18 50 =32961.5 Revenue of Ge Alumt produchon Cost formenting cotm For emantim time x Hand wco Ham d a im De beoring Cosd |m :t i40 0.37 X9.so+0.30 x s75+0.40 x7.90- $9.3 Simloy predueton cot Geun (umit O43X9.5o 8-25 x S75 +0.27 x 7.90-9. 1955 nrocduce cos of Geaclumt O45 X1.5o +0.31x875 +0.42 x7.10=10-30SS produs coy mot Gea DUnit 0.S2 a.So to.40,x 875 0.3o X7.10-0.168 Eudy outshst Atcost Dema mareat Cest -1.3 Gea A 9.20 나00 ast .75 Gear B 235 $ 10.s65 450 11.00 965 Geo c 2sh 우65 S11.79 10.168 550 Gea D 550 500 brt fosmnt pertent Capacty No.0f Goss Can fermed of Ga tpe 037 6.43 t0.s2 t0.45 Cs Scanned with CamScanner 232 4g 282 Ge

Simidap NO of Geas Ca Hund of eoth type O.300.3s to.3( t6.40 314.463 3子 Gesy Novof Gec of e 400 Cor Dem O.40t0.37+0.y24032 264.90 S G Comsidy Cimp, Prele G tue sefed Tote 26T Conmicritof each type CS Scanned with CamScanner

Buy butdod (408 9.24) Tot cost (1.2 K25) (4.145 26 (236x9.3 (lo 30SS 2 (to. 968 x2 Totaf cort 21754 Totol proft fasumme Toty cot (mtg Jouestind 3297.5 - $ 2 1F4 Total profi 11213.S () By im cras A hau n Detert depomter m Hhevs t mffpre me d whe Otfene depatmar sm TAL Hene De y depatmt te ee ime wil imcra praf Formtng RHaly deps hst Complety c sh maas 265 Ges H pries imeres Cos fer Gear D Nov Cot OS2 X9. t 0.40 X 12.6 o.3 2 x 7.10 12.268 11.75 oT to precure. 550. Gead D S0 amd ISD 40 mamufacture 1S0 Amswer CS Scanned with CamScanner