Question

Bolse Lumber has decided to enter the lucrative prefabricated housing business. Erity, it plans to offer three models: standard deluxe, and Rury. Each house is precated and partially came the My Notes factory, and the final assembly is completed on site. The dollar amount of building material required, the amount of labor required in the factory for prefabrication and partial asset the amount of one labor required, and the profit per unit are as follows Standard Model Deluxe Model Luxury Model Material $6.000 50.000 Factory Labor (hr) on site Labor (hr) 180 210 300 Proll $3,400 $4.000 95.000 For the first year's production, a sum of $8,200.000 is budgeted for the building material the number of labor hours available for work in the factory is not to exceed 215.000 hr and the amount of labor for on-site work is to be less than or equal to 237.000 labor hours. Determine how many houses of each type Bolse should produce tomadimize its prefit from this new venture standard model deluxe model luxury model

Answer 1

Let number of standard model’s houses: x

number of deluxe model’s houses: y

number of luxury model’s houses: z

Find the inequalities based on the given information.

6000x+8000y+10,000z≤8,200,000

240x+220y+200z≤215,000

180x+210y+300≤237,000

Solve using solver in excel.

Enter the given data in excel.

0 standard Model Deluxe Model Luxury Model total 6000 8000 10000 240 220 200 210 4000 5000 Material Factory Labor (hr) ON-site Labor(hr) Profit Maximum capacity 8200000 215000 237000 0 300 180 3400 0 0

In total column put the formula for the left hand side of the constraints.

For example, for material put the formula =C4*C2+D4*D2+E4*E2 where

C4 has material required for 1 standard model.

C2 is the variable for the number of standard models.

D4 has material required for 1 deluxe model.

D2 is the variable for the number of deluxe models.

E4 has material required for 1 luxury model.

E2 is the variable for the number of luxury models.

Similarly, for factory labor put the formula =C5*C2+D5*D2+E5*E2

for ON site labor put the formula =C6*C2+D6*D2+E6*E2

for profit put the formula =C7*C2+D7*D2+E7*E2

Open solver and set the objective at the total profit cell and select maximize, then add constraints.

Solver Parameters Set Objective: $F$7 То: Омах O Min O Value of: By Changing Variable Cells: $C$2:$E$2 Subject to the Constraints: $F$4 <= $G$4 $F$5 <= $G$5 $F$6 <= $G$6 Add Change Delete Reset All Load/Save Make Unconstrained variables Non-Negative Select a Solving Method: GRG Nonlinear Options Solving Method Select the GRG Nonlinear engine for Solver Problems that are smooth nonlinear. Select the LP Simplex engine for linear Solver Problems, and select the Evolutionary engine for Solver problems that are non-smooth. Help Solve Close

press enter to get the values.

275 300 415 standard Model Deluxe Model Luxury Model total Maximum capacity Material 6000 8000 10000 8200000 8200000 Factory Labor (hr) 240 220 200 215000 215000 ON-site Labor(hr) 180 210 300 237000 237000 Profit 3400 4000 5000 4210000

So, number of standard model = 275

number of deluxe model = 300

Number of luxury model= 415