Homework #2 Name: _____________________________ Show your work/steps and specify the units ($, %, days, etc.) for your answers to receive full credit.
(1) An architect firm uses an average of 60 boxes of copier paper a day. The firm operates 280 days a year. Storage and handling costs for the paper are $30 a year per box, and its costs approximately $60 to order and receive a shipment of paper.
(a) What quantity order size would minimize the total annual inventory cost? ________________________________________________________________________________
(b) Determine the minimum total annual inventory cost. ________________________________________________________________________________
(c) The office manager is currently using an order size of 300 boxes. The partners of the firm expect the office to be managed “in a cost-efficient manner.” Would you recommend the manager to use your quantity from part (a) rather than 300 boxes? _______.
Justify your answer (by determining the total annual inventory cost for 300 boxes): ________________________________________________________________________________
(2) The ABC Company is both a producer and a user of brass couplings. The firm operates 220 days a year and uses the couplings at a steady rate of 60 per day. Coupling can be produced at a rate of 200 per day. Annual storage cost is $2 per coupling, and machine setup cost is $120 per run. Determine the:
(a) optimal production run size = ________________________________________________________ (b) length of production run = ___________________________________________________________ (c) maximum inventory level = __________________________________________________________
(3) Suppose that a perishable item costs $8 and sells for $10. Any item that is not sold by the end of the day can all be sold at $5.
(a) Find MP = and ML = . The table below reveals the discrete demand for this item. (b) Complete the last column of the table.
Demand P(Demand = this level) P(Demand this level) 110 0.20
120 0.15
130 0.15
140 0.15 150 0.15 160 0.10 170 0.05 180 0.05
(c) Use the marginal analysis to determine how many units should be stocked.
Analysis: ________________________________________________________________________ Conclusion: ________________________________________________________________________
(4) ABC Woodcarving manufactures two types of wooden toys: soldiers and trains. A soldier sells for $29 and uses $10 worth of raw materials. Each soldier that is manufactured increases ABC’s variable labor and overhead costs by $12. A train sells for $22 and uses $7 worth of raw materials. Each train built increases ABC’s variable labor and overhead costs by $10. The manufacture of wooden soldiers and trains requires two types of skilled labor: carpentry and finishing. A soldier requires 4 hours of finishing labor and 3 hour of carpentry labor. A train requires 2 hour of finishing and 1 hour of carpentry labor. Each month, ABC can obtain all the needed raw material but only 4,200 finishing hours and 2,000 carpentry hours. Demand for trains is unlimited, but at most 220 trains are bought each month. ABC wants to maximize monthly profit (revenues – costs). Formulate an LP model that can be used to maximize ABC’s monthly profit.
(a) Step 1: Define the decision variables precisely and completely (e.g., let X1 = … and X2 = …, etc.).
__________________________________________________________________________________________
__________________________________________________________________________________________ (b) Step 2: State the objective function.
___________________________________________________________________________________________ (c) Step 3: Specify the constraints.
___________________________________________ ______________________________________________________________________________________
___________________________________________ ___________________________________________ ___________________________________________
(5) Consider the following linear programming model with 4 regular constraints:
Maximize 3X + 5Y subject to: 4X + 4Y ≤ 48 4X + 3Y ≤ 50 2X + 1Y ≤ 20
X ≥ 2 X, Y ≥ 0
(a) Draw your graph in the space below:
(constraint #1)
(constraint #2)
(constraint #3)
(constraint #4) (non-negativity constraints)
(a) Which of the constraints is redundant? Constraint #______. Justify by drawing a graph similar to Figure 7.14 on p.263.
(b) Is point (9,3) a feasible solution? _____. Explain your answer (by analyzing each of the constraints). Constraint #1: _______________________________________________________________ Constraint #2: _______________________________________________________________ Constraint #3: _______________________________________________________________ Constraint #4: _______________________________________________________________
(c) Which of the following points yields the best solution? Underline the best solution: (7,5), (9,2), (6,6). Justify your answer (using the data from the above LP model).
(7,5): ____________________________________________________________________ (9,2): ____________________________________________________________________ (6,6): ____________________________________________________________________
