Question

The Silver Star Bicycle Company will be manufacturing both men's and women's models of its Easy-Pedal 10-speed bicycles during the next two months. Management wants to develop a production schedule indicating how many bicycles of each model should be produced in each month. Current demand forecasts call for 150 men's and 125 women's models to be shipped during the first month and 210 men's and 160 women's models to be shipped during the second month. Additional data are shown: Production Current Labor Requirements (hours) Manufacturing Assembly Model Costs Inventory Men's $160 2.0 1.5 20 Women's $130 1.3 1.3 30 Last month the company used a total of 1000 hours of labor. The company's labor relations policy will not allow the combined total hours of labor (manufacturing plus assembly) to increase or decrease by more than 100 hours from month to month. In addition, the company charges monthly inventory at the rate of 2% of the production cost based on the inventory levels at the end of the month. The company would like to have at least 25 units of each model in inventory at the end o the two months. a. Establish a production schedule that minimizes production and inventory costs and satisfies the labor-smoothing, demand, and inventory requirements. What inventories will be maintained, and what are the monthly labor requirements? If required, round your answers to the nearest whole number. Production schedule: The optimal solution is to produce 187 of the men's model in month 1, 178 of the men's model in month 2, 95 units of the women's model in month 1, and 185 of the women's model in month 2. Total Cost = $ 95126 Inventory Schedule Month 1 57 Men's o Women's Month 2 25 Men's 25 Women's Labor Levels Previous month 1000 hours Month 1 900 hours Month 2 1106 hours
please answer all of B and my answers for part A are correct.

Answer 1

Answer b: The optimal solution is to produce Men's model in month 1 201 Men's model in month 2 164 Women's model in month 1 95 Women's model in month 2 185 Total cost $ 95,172.00 Cost will increase by (95172-95126) $ 46.00 I recommend option a with combined totallabour hours (manufacturing + assembly) are allowed to increase by 100 hours

Minimize: LP model formulation Let: X11 = amount of men's model in month 1 X21 = amount of women's model in month 1 x12 = amount of men's model in month 2 X22 = amount of women's model in month 2 S11 = inventory of men's model at end of month 1 s21 = inventory of women's model at end of month 1 S12 = inventory of men's model at end of month 2 S22 = inventory of women's model at end of month Calculations: Monthly inventory rate 2% of 160=3.2 2% of 130=2.6

LP model formulation Minimize: 160x11 + 130x21 + 160x12 + 130x22 + 3.2s11 + 2.6s21 + 3.2s12 + 2.6s22 s.t. x11 - 511 = 130 Satisfy Demand [1] X21 - 521 = 95 Satisfy Demand [2] s11 + x12 - 512 = 210 Satisfy Demand [3] s21 + x22 - s22 = 160 Satisfy Demand [4] s12 > 25 Ending Inventory [5] $22 > 25 Ending Inventory [6] Labor Hours: Men's = 2.0 + 1.5 = 3.5 Women's = 1.3 + 1.3 = 2.6 3.5 x11 + 2.6 x21 > 950 Labor Smoothing for [7] 3.5 x11 + 2.6 x21 < 1050 Month 1 [8] 3.5 x11 + 2.6 x21 - 3.5 x12 - 2.6 x22 < 50 Labor Smoothing for [9] -3.5 x11 - 2.6 x21 + 3.5 x12 + 2.6 x22 < 50 Month 2 [10] x11, X12, X21, x22, 511, s12, s21, s22 > 0

Enter data>add formulas>go to datatab>solver>add constraints>solve B с - E D F G H J к L M N o Р Q R S Problem setup area X11 X21 160 1 0 А 9 10 Data 11 12 Objective 13 Constraint 1 14 Constraint 2 15 Constraint 3 16 Constraint 4 17 Constraint 5 18 Constraint 6 19 Constraint 7 20 Constraint 8 21 Constraint 9 22 Constraint 10 23 24 Results 25 Variables 26 Objective 27 0 0 0 이 3.5 3.5 3.5 -3.5 x12 130 0 1 0 0 0 0 2.6 2.6 2.6 -2.61 X22 160 0 0 1 0 0 0 0 0 -3.5 3.5 s11 130 0 0 0 1 0 0 0 0 -2.6 2.6 s21 3.2 -1 ol 1 ol ol 0 ol 01 ol s12 2.6 0 -1 0 1 0 0 0 0 0 ol s22 3.2 0 이 - 1 0 1 0 0 0 2.61 0/= 0= 0= -1 = 0 > 1 > 01> 01< ols 01> 0 130 95 210 160 25 25 950 1050 50 50 Results LHS Slack/Surplus 95171.74 130 0 95 0 210 0 160 0 25 0 25 0 950 0 950 100 -105.5 155.4999733 105.5 -55.4999733 < constraints > constraints 130 130 130 95 95 95 210 2100 210 160 160 160 0 0 25 0 0 25 0 0 950 9501 1050 0 -105.5 50 0 0 0 105.5 130 95 210 160 25 25 950 0 0 50 0 0 0 201 95 164 185 71 0 25 25 95172

Add Constraints Solver Parameters Х Set Objective: SMS121 1 To: Омах O Min O Value of: 0 By Changing Variable Cells: $B$25:51$25 Subject to the Constraints: SP$13:5P522 <= $Q$13:5Q822 $R$13:$R$22 >= $S$13:$S$22 Add 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 Close

Formulas in excel A B с D E F G H J K L M N 16 Constraint 4 9 10 Data 11 12 Objective 10 13 Constraint 1 14 Constraint 2 15 Constraint 3 17 Constraint 5 Iconstraint a 18 Constraint 6 19 Constraint 7 onstraint 29 20 Constraint 8 21 Constraint 9 22 Constraint 10 23 24 Results 25 Variables 26 Objective 27 1 x11 X21 x12 X22 s11 s21 s12 Is22 160 130 160 130 3.200000 2.59999990463256 3.20000004768371 2.59999990463256 11 0 0 0 -1 0 0 10 O 1 0 10 In .1 -1 0 10 10 0 1 n 0 1 11 O -1 To in 10 0 V 0 in 1 0 In U -1 lo 0 0 o 0 0 19 10 11 0 10 0 0 0 lo 0 lo U 0 0 0 3.5 2.59999990463256 0 lo 0 0 0 0 3.5 2.59999990463256 0 lo lo 0 0 Jo 3.5 2.59999990463256 -3.5 -2.59999990463256 0 0 0 Jo -3.5 -2.59999990463256 3.5 2.59999990463256 0 0 10 lo 0 = 130 95 210 160 > 25 > 25 > 1950 < 1050 <50 > 50 Results LHS Slack/Surplus =SUMPRODUCT(B12:112,$B$25 $1$25) =SUMPRODUCT(B13:113,$B$25:$1$25) = 13-M13 =SUMPRODUCT(B14:114,$B$25:$1$25) = 14-M14 -SUMPRODUCT(B15:115,$B$25 $1$25) = 15-M15 =SUMPRODUCT(B16:116,$B$25 $1$25) EK16-M16 =SUMPRODUCT(B17:117 $B$25 $1$25) =K17-M17 =SUMPRODUCT(B18:118,$B$25 $1$25) = 18-M18 =SUMPRODUCT(B19:119.$B$25:$I$25) =K19-M19 =SUMPRODUCT(B20:120,$B$25:$1$25) =K20-M20 =SUMPRODUCT(B21:121,$B$25:$I$25)=K21-M21 =SUMPRODUCT(B22:122 $B$25:$1$25)=K22-M22 1 200.95 164. 185 70.857140 25 25 =M12