Case Problem LP: Special Products Jim Kelley is in charge of production planning at Special Products. The company produces three models of their special product that are assembled using components purchased from outside suppliers. The company works 5 days a week and 8 hours each workday. Production might be limited by market demand, the assembly capacity at several departments and the availability of certain critical components. Market demand during the planning period is limited to 400 units/week of Model SL, 500 units/week of Model GL and 300 units/week of Model LX. The company has firm contracts with vendors to supply minimum quantities of 100 units/week of Model SL, 150 units/week of Model GL, and 100 units/week of Model LX. Besides supplying the minimum amounts, the company would like to make as many more of each model as it can, up to the market limits. Profit margins on the three models are ₱7,500 on Model SL, ₱5,000 on Model GL and ₱10,000 on Model LX. Model SL takes 5 minutes to assemble at shop 1, 4 minutes at shop 2 and 2 minutes at shop 3. Model GL takes 4 minutes to assemble at shop 1, 2 minutes at shop 2 and 6 minutes at shop 4. Model LX takes 3 minutes to assemble at shop 1, 4 minutes at shop 3 and 10 minutes at shop 5. The daily capacities of the 5 shops are limited by the availability of the workforce and equipment to the following hours per day: Shop Shop Capacity (Hours/Day) 1 12 2 14 3 8 4 12 5 10 Model SL uses a special microchip (A) whose supply is limited to 500/week. Model GL uses the same microchip as Model SL and a second microchip (B) whose supply is limited to 400/week. Model LX uses a microchip (C) that's not used in either of the other model; its supply is limited to 600/week. a. How many units of each model should be scheduled for production each week and what will be the weekly profit? b. What constraints limit profit? c. Should Kelley consider increasing capacity at any of the assembly shops? If so, which ones?
Case Problem LP: Special Products
Jim Kelley is in charge of production planning at Special Products. The company produces three models of their special product that are assembled using components purchased from outside suppliers. The company works 5 days a week and 8 hours each workday. Production might be limited by market demand, the assembly capacity at several departments and the availability of certain critical components.
Market demand during the planning period is limited to 400 units/week of Model SL, 500 units/week of Model GL and 300 units/week of Model LX. The company has firm contracts with vendors to supply minimum quantities of 100 units/week of Model SL, 150 units/week of Model GL, and 100 units/week of Model LX. Besides supplying the minimum amounts, the company would like to make as many more of each model as it can, up to the market limits. Profit margins on the three models are ₱7,500 on Model SL, ₱5,000 on Model GL and ₱10,000 on Model LX.
Model SL takes 5 minutes to assemble at shop 1, 4 minutes at shop 2 and 2 minutes at shop 3. Model GL takes 4 minutes to assemble at shop 1, 2 minutes at shop 2 and 6 minutes at shop 4. Model LX takes 3 minutes to assemble at shop 1, 4 minutes at shop 3 and 10 minutes at shop 5. The daily capacities of the 5 shops are limited by the availability of the workforce and equipment to the following hours per day:
| Shop | Shop Capacity (Hours/Day) |
| 1 | 12 |
| 2 | 14 |
| 3 | 8 |
| 4 | 12 |
| 5 | 10 |
Model SL uses a special microchip (A) whose supply is limited to 500/week. Model GL uses the same microchip as Model SL and a second microchip (B) whose supply is limited to 400/week. Model LX uses a microchip (C) that's not used in either of the other model; its supply is limited to 600/week.
a. How many units of each model should be
b. What constraints limit profit?
c. Should Kelley consider increasing capacity at any of the assembly shops? If so, which ones?
d. Should Kelley consider looking for additional suppliers of any of the three special microchips? If so, which ones?
e. Should Special Products' marketing director be urged to promote the models more aggressively in order to increase market demand? If so, which ones?
Special Products' board of directors is looking for ways to increase profit. They would like answers to the following questions:
f. Would increasing the capacity of any production facilities be a wise move? Comment on what's good and what's bad about any increases and what additional actions might need to be taken to increase capacity successfully.
g. How would the responses to parts (a) and (b) change if the supply of chip A was increased by 50%?
h. How would the responses to parts (a) and (b) change if, in addition to the 50% increase in the supply of chip A. the markets for Models SL and LX was inceased by 50% for each?
i. How would the responses to parts (a) and (b) change if, in addition to a 50% increase in the supply of chip A and a 50% increase in the markets for Models SL and LX, the capacity of shop 1 was increased by 50%?
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