Weasley\'s Wizard Wheezes will be manufacturing Product A and Product B, which b
ID: 360597 • Letter: W
Question
Weasley's Wizard Wheezes will be manufacturing Product A and Product B, which belong to their WonderWitch product line, during the next 2 months. Management wants to develop a production schedule indicating how many products should be produced in each month. Demand forecasts call for 150 Product A units and 125 Product B units to be shipped during the first month and 200 Product A units and 150 Product B units during the second month. Customer satisfaction is very important for Weasley Brothers, therefore management wants to make sure the total demand is covered for both products. Management has additional data for Product A and Product B. Production Cost (sickles) 120 90 Labor Requirements (hours) Manufacturing Current Inventory 20 30 Product Type 2.0 1.6 Assembly 1.5 1.0 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 a 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 product type at the end of the 2 months. The management wants to establish a production schedule (amount of products produced every month) that minimizes production and inventory costs and satisfies the labor, demand, and inventory requirements. Formulate this problem as a linear program: a) Define the decision variables. b) Write down the objective function and describe it in words. c) Write down the constraints and describe each of them in words. d) Use Excel solver to find the optimal production schedule and its corresponding total cost.Explanation / Answer
a) Let us assume that the number of units of product A produced in first month is A1 and in 2nd month be A2
and the number of units of product B produced in firsr month is B1 and in 2nd month is B2
We need to find out the values of A1, A2, B1 and B2 so that the the company can achieve minimum production and inventory cost without violating any constraints .
Therefore, A1, B1, A2 and B2 are our decision variables.
b) The objective function is to minimize the total production and total inventory cost.
Production cost of A in first month = 120A1
Production cost of B in first month = 90B1
Total Production cost in first month= 120A1 + 90B1
Inventory of A at the end of first month = (A1+20-150)
Therefore, Inventory cost for A = (A1+20-150)x(120x0.02) = 2.4 (A1-130)
Inventory of B at the end of first month = (B1+30-125)
Therefore, inventory cost of B = (B1-95)x(90X0.02) = 1.8 (B1-95)
Therefore, total inventory cost for first month = (2.4A1 - 312 + 1.8B1 - 171) = 2.4A1+1.8B1-483
Therefore, total cost in first month = 120A1 + 90B1 + 2.4A1 + 1.8B1 - 483
Total Cost in first month = 122.4A1 + 91.8B1 -483
Second Month:
Production cost of A = 120A2
Production cost of B = 90B2
Total Production cost = 120A2 + 90B2
Inventory of A at the end of 2nd month = (A2 + A1-130 - 200) = (A1+A2-330)
Inventory cost of A = 2.4 (A1+A2-330)
Inventory of B at the end of 2nd month = (B2+ B1-95-150)
Inventory cost of B in the 2nd month = 1.8 (B1+B2 - 245)
Total inventory cost at the end of 2nd month = 2.4A1 + 2.4A2 + 1.8B1 +1.8B2-792-441
= 2.4A1 + 2.4A2 + 1.8B1 +1.8B2 - 1233
Total cost at the end of 2nd month = 120A2+ 90B2+ 2.4A1 +2.4A2 + 1.8B1 +1.8B2 - 1233
Therefore, Total cost incurred = 124.8A1 + 93.6B1 + 122.4A2 + 91.8B2 - 1716
This is the objective function.
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