Question

EZ-Windows, Inc., manufactures replacement windows for the home remodeling business. In January, the company produced 15,000 windows and ended the month with 10,000 windows in inventory. EZ-Windows’ management team would like to develop a production schedule for the next three months. A smooth production schedule is obviously desirable because it maintains the current workforce and provides a similar month-to-month operation. However, given the sales forecasts, the production capacities, and the storage capabilities as shown, the management team does not think a smooth production schedule with the same production quantity each month is possible.

EZ-Windows, Inc., manufactures replacement windows for the home remodeling business. In January, the company produced 15,000 windows and ended the month with 10,000 windows in inventory. EZ-Windows’ management team would like to develop a production schedule for the next three months. A smooth production schedule is obviously desirable because it maintains the current workforce and provides a similar month-to-month operation. However, given the sales forecasts, the production capacities, and the storage capabilities as shown, the management team does not think a smooth production schedule with the same production quantity each month is possible. February March April Sales forecast 15,000 15,500 20,500 Production capacity 13,000 15,000 17,000 Storage capacity 6,000 6,000 6,000 The company’s cost accounting department estimates that increasing production by one window from one month to the next will increase total costs by $1.00 for each unit increase in the production level. In addition, decreasing production by one unit from one month to the next will increase total costs by $0.65 for each unit decrease in the production level. Ignoring production and inventory carrying costs, formulate and solve a linear programming model that will minimize the cost of changing production levels while still satisfying the monthly sales forecasts. If required, round your answers to two decimal places. If an amount is zero, enter "0". Let: F = number of windows manufactured in February M = number of windows manufactured in March A = number of windows manufactured in April Im = increase in production level necessary during month m Dm = decrease in production level necessary during month m sm = ending inventory in month m Min I1 + I2 + I3 + D1 + D2 + D3 s.t. (1) F - s1 = February Demand (2) s1 + M - s2 = March Demand (3) s2 + A - s3 = April Demand (4) F - I1 + D1 = Change in February Production (5) M - F - I2 + D2 = Change in March Production (6) A - M - I3 + D3 = Change in April Production (7) F ≤ February Production Capacity (8) M ≤ March Production Capacity (9) A ≤ April Production Capacity (10) s1 ≤ February Storage Capacity (11) s2 ≤ March Storage Capacity (12) s3 ≤ April Storage Capacity If required, round your answers to the nearest dollar. Cost: $   If required, round your answers to the nearest whole number. If an amount is zero, enter "0" February March April Production Level Increase in Production Decrease in Production Ending Inventory

The company’s cost accounting department estimates that increasing production by one window from one month to the next will increase total costs by $1.00 for each unit increase in the production level. In addition, decreasing production by one unit from one month to the next will increase total costs by $0.65 for each unit decrease in the production level. Ignoring production and inventory carrying costs, formulate and solve a linear programming model that will minimize the cost of changing production levels while still satisfying the monthly sales forecasts. If required, round your answers to two decimal places. If an amount is zero, enter "0".

Let:

F = number of windows manufactured in February

M = number of windows manufactured in March

A = number of windows manufactured in April

I_m = increase in production level necessary during month m

D_m = decrease in production level necessary during month m

s_m = ending inventory in month m

Answer 1

Attached are the constraints and Opitmization equation to solve in the solver

Min 1*1, +1*1, +1*1, + 0.65*D, + 0.65*D, +0.65*D, s.t. -1 F-S 1+10000=15000 February Demand -CION 13000 F-S 1=5000 -2 s, + M -8, = 15500 -3 S2 + A-S, = 20500 -4 F -1, +D = 15000 -5M - F -1, + D, = 0 -6 A - M -13 + D3 = 0 -ZF S 13000 -8 M = 15000 -9 A 17000 -10 s, < 6000 -11 s, 56000 -12 sz s 6ooo March Demand April Demand Change in February Production Change in March Production Change in April Production February Production Capacity March Production Capacity April Production Capacity February Storage Capacity March Storage Capacity April Storage Capacity 15000 17000 6000 6000 6000