Using the data above. Fill in the cells accordingly. Do not have to solve. You may have to zoom in to see cells.

Dart Machinery produces heads for engines used in the manufacture of trucks. The production line is very complex. Two types of engine heads are produced on this line: the P model and the H model. The H model is used in heavy-duty trucks and the P model is used in smaller trucks. Because only one model can be produced at a time, the line is set up to manufacture either the P model or the H model, but not both. When the model is produced, there is $500 in production set-up costs. When set up for the P model, the maximum production rate is 100 units per week. When set up for the H model, the maximum production rate is 80 units per week. The manager at Dart Machinery has asked you to help plan the production schedule for the next several weeks. Currently, the inventory consists of 125 P-model heads and 143 H-model heads. Inventory carrying costs are estimated as $40/unit for the P-model and $60/unit for the H-model. Production costs are $225/unit for the P-model and $310/unit for the H-model. The objective is to develop a weekly production schedule that minimizes the sum of the production cost, plus inventory carrying cost, plus production set-up cost. The product demand schedule, based on the requirements of an engine assembly plant, is shown in Table 1. Safety stock requirements are such that week-ending inventory must provide for at least 80% of the next week's demand. Assume that no inventory carryover is needed after week 9. To develop the optimum production schedule, you will integrate a network model with binary programming model. Here are examples of the decision variables in the LP model: Pia - units of P model produced in week 1 ha = units of H model produced in week 1 h = binary decision variable (= 1 if H model units are produced, = 0 if P model units are produced) Pat = units of P model carried over in inventory at end of week 1 hab = units of H model carried over in inventory at end of week 1 Table 1. Product demand and safety stock requirements. Product Demand 80% Product Demand Week P model H model P model H model 1 55 40 2 55 40 44 32 3 30 36 24 4 0 0 0 0 5 45 45 36 36 6 45 50 36 40 7 35 60 28 48 8 35 55 28 44 9 35 60 28 48 45 A B S decision variables: C D E F G H Weekly production quantities, P-model (# units) p2b p3c pid p5e p6f p9i L M N 0 P Q R Weekly production quantities, H-model (# units) h2b h3c hdd h5e hof h7g h8h pia pg pah hia h9i objective coefficients: S/unit s/unit S/unit s/unit S/unit s/unit S/unit S/unit S/unit S/unit s/unit S/unit S/unit S/unit S/unit S/unit S/unit s/unit constraints: Demand constraints for P-model, IN (production + previous inventory) = OUT (demand in rentor carried over to next week) week #1 (A) week #2 (B) week #3 (C) week #4 (D) week #5 (E) week #6 (F) week #7 (G) week #8 (H) week #9 (0) Demand constraints for H-model, IN (production + previous inventory) = OUT (demand + inventory carried over to next week) week #1 (A) week #2 (B) week #3 (C) week #4 (D) week #5 (E) week #6 (F) week #7 (G) week #8 (H) week #9 (0) T U AA AB AT AU V W Y Z BINARY - H-model production h3 14 h5 h6 h7 AC AD AE AF AG AH AU Inventory carryover at end of week, P-model (#units) pab pbc pod pde pef pfg pgh phi AK AL AM AN AO AP AQ AR Inventory carryover at end of week, H-model (# units) hab hbc hod hde hef hfg hgh hhi hi h2 h8 h9 $ $ $ $ $ $ $ $ $ S/unit S/unit s/unit S/unit S/unit Sunit s/unit S/unit S/unit s/unit s/unit S/unit S/unit s/unit S/unit S/unit COST(S): LHS RHS LHS RHS LHS RHS Production limit for P-model (100 units/week) week #1 week #2 week #3 week #4 week #5 week #6 week #7 week #8 week #9 Production limit for H-model (80 units/week) week #1 week #2 week #3 week #4 week #5 week #6 week #7 week #8 week #9 Safety stock requirement for P-model (end of week inventory must provide at least 80% of next week's demand) week #1 (A) week #2 (B) week #3 (C) week #14 (D) week #5 (E) week #6 (F) week #7 (G) week #8 (H) Safety stock requirement for H-model (end of week inventory must provide at least 80% of next week's demand) week #1 (A) week #2 (B) week #3 (C) week #4 (D) week #5(E) week #6 (F) week #7 (G) week #8 (H) T U AA AB AE AS AT AU VW Y Z BINARY -- H-model production h3 h4 h5 h6 h7 AC AD AF AG AH AI AU Inventory carryover at end of week, P-model (# units) pab pbc pod pde pfg pgh phi AK AL AM AN AO AP AR Inventory carryover at end of week, H-model (# units) hab hbc hod hde hef hfg hhi hi h2 h8 h9 pef hgh LHS RHS LHS RHS LHS RHS Dart Machinery produces heads for engines used in the manufacture of trucks. The production line is very complex. Two types of engine heads are produced on this line: the P model and the H model. The H model is used in heavy-duty trucks and the P model is used in smaller trucks. Because only one model can be produced at a time, the line is set up to manufacture either the P model or the H model, but not both. When the model is produced, there is $500 in production set-up costs. When set up for the P model, the maximum production rate is 100 units per week. When set up for the H model, the maximum production rate is 80 units per week. The manager at Dart Machinery has asked you to help plan the production schedule for the next several weeks. Currently, the inventory consists of 125 P-model heads and 143 H-model heads. Inventory carrying costs are estimated as $40/unit for the P-model and $60/unit for the H-model. Production costs are $225/unit for the P-model and $310/unit for the H-model. The objective is to develop a weekly production schedule that minimizes the sum of the production cost, plus inventory carrying cost, plus production set-up cost. The product demand schedule, based on the requirements of an engine assembly plant, is shown in Table 1. Safety stock requirements are such that week-ending inventory must provide for at least 80% of the next week's demand. Assume that no inventory carryover is needed after week 9. To develop the optimum production schedule, you will integrate a network model with binary programming model. Here are examples of the decision variables in the LP model: Pia - units of P model produced in week 1 ha = units of H model produced in week 1 h = binary decision variable (= 1 if H model units are produced, = 0 if P model units are produced) Pat = units of P model carried over in inventory at end of week 1 hab = units of H model carried over in inventory at end of week 1 Table 1. Product demand and safety stock requirements. Product Demand 80% Product Demand Week P model H model P model H model 1 55 40 2 55 40 44 32 3 30 36 24 4 0 0 0 0 5 45 45 36 36 6 45 50 36 40 7 35 60 28 48 8 35 55 28 44 9 35 60 28 48 45 A B S decision variables: C D E F G H Weekly production quantities, P-model (# units) p2b p3c pid p5e p6f p9i L M N 0 P Q R Weekly production quantities, H-model (# units) h2b h3c hdd h5e hof h7g h8h pia pg pah hia h9i objective coefficients: S/unit s/unit S/unit s/unit S/unit s/unit S/unit S/unit S/unit S/unit s/unit S/unit S/unit S/unit S/unit S/unit S/unit s/unit constraints: Demand constraints for P-model, IN (production + previous inventory) = OUT (demand in rentor carried over to next week) week #1 (A) week #2 (B) week #3 (C) week #4 (D) week #5 (E) week #6 (F) week #7 (G) week #8 (H) week #9 (0) Demand constraints for H-model, IN (production + previous inventory) = OUT (demand + inventory carried over to next week) week #1 (A) week #2 (B) week #3 (C) week #4 (D) week #5 (E) week #6 (F) week #7 (G) week #8 (H) week #9 (0) T U AA AB AT AU V W Y Z BINARY - H-model production h3 14 h5 h6 h7 AC AD AE AF AG AH AU Inventory carryover at end of week, P-model (#units) pab pbc pod pde pef pfg pgh phi AK AL AM AN AO AP AQ AR Inventory carryover at end of week, H-model (# units) hab hbc hod hde hef hfg hgh hhi hi h2 h8 h9 $ $ $ $ $ $ $ $ $ S/unit S/unit s/unit S/unit S/unit Sunit s/unit S/unit S/unit s/unit s/unit S/unit S/unit s/unit S/unit S/unit COST(S): LHS RHS LHS RHS LHS RHS Production limit for P-model (100 units/week) week #1 week #2 week #3 week #4 week #5 week #6 week #7 week #8 week #9 Production limit for H-model (80 units/week) week #1 week #2 week #3 week #4 week #5 week #6 week #7 week #8 week #9 Safety stock requirement for P-model (end of week inventory must provide at least 80% of next week's demand) week #1 (A) week #2 (B) week #3 (C) week #14 (D) week #5 (E) week #6 (F) week #7 (G) week #8 (H) Safety stock requirement for H-model (end of week inventory must provide at least 80% of next week's demand) week #1 (A) week #2 (B) week #3 (C) week #4 (D) week #5(E) week #6 (F) week #7 (G) week #8 (H) T U AA AB AE AS AT AU VW Y Z BINARY -- H-model production h3 h4 h5 h6 h7 AC AD AF AG AH AI AU Inventory carryover at end of week, P-model (# units) pab pbc pod pde pfg pgh phi AK AL AM AN AO AP AR Inventory carryover at end of week, H-model (# units) hab hbc hod hde hef hfg hhi hi h2 h8 h9 pef hgh LHS RHS LHS RHS LHS RHS