Question

1. Northwoods Backpackers is a retail catalog store in Vermont that specializes in outdoor clothing and camping equipment. Phone orders are taken each day by a large pool of computer operators, some of whom are permanent and some temporary. A permanent operator can process an average of 76 orders per day, whereas a temporary operator can process an average of 53 orders per day. The company averages at least 600 orders per day. The store has 10 computer workstations. A permanent operator processes about 3 orders with errors each day, whereas a temporary operator averages 4.1 orders with errors daily. The store wants to limit errors to 24 per day. A permanent operator is paid $81 per day, including benefits, and a temporary operator is paid $50 per day. The company wants to know the number of permanent and temporary operators to hire to minimize costs.

Answer 1

Let the no. of permanent operators be “x” and temporary operators be “y”.

Total costs = 70x+50y. This is the objective function and has to be minimized.

Constraints:

1. 76x+53y>=600

2. x+y <= 10

3. 3x+4.5y<=24

4. x,y>=0 and should be integers

Using the solver function in excel the following solution is obtained:

x	8.00
y	0.00
				Formula
Total costs	560.00			70x+50y
Constraints
608.00	>=	600.00		76x+53y>=600
8.00	<=	10.00		x+y <= 10
10.40	<=	24.00		3x+4.5y<=24

Thus minimized cost = $560 and the company will hire 8 permanent workers and 0 temporary workers. All constraints are satisfied. No. of orders processed = 608 (>600), no. of computer workstations used = 8(<10) and no. of errors = 10.4 (<24).

Solver image:

Clear 2 Show Detail ? Solver 21 AF Solver Parameters Connections Properties e Edit Links Connections 21 Sort Filter Reapply Advanced Text to Remove Data Columns Duplicates Validation Sort & Filter Set Objective: $K$5 P To: O Max Min O Value of: 8.00 0.00 By Changing Variable Cells: SK$2:$K$3 Total cost 550.00 Formula 70x+50y Subject to the Constraints: $J$10 <= 24 $J$8 >= 600 Add 600 Constraints 608 > 8 <= 10.4 <= 76x+53y>=600 x+y<=10 3x+4.5y<=24 SK$2:$K$3 = integer SK$2:$K$3 >= 0 Change Delete Reset All Load/Save Make Unconstrained variables Non-Negative Select a Solving Method: Simplex LP 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