COMPUTER PRODUCTION
MVE Enterprises can manufacture four different computer models; the Student, Plus, Net, and Pro models. The following gives the configurations of each model:
STUDENT PLUS NET PRO
Processor Celeron Celeron Celeron Pentium
Hard Drive 20 gb 20 gb 20 gb 30 gb
Floppy Drives 1 1 2 1
Zip Drives Yes Yes No Yes
Audio/Video CD R/W DVD DVD +
CD R/W DVD +
CD R/W
Monitor 15” 15” 17” 17”
Case Tower Mini-
Tower Mini-
Tower Tower
Production
Time (hrs.) .4 .5 .6 .8
Unit Profit $70 $80 $130 $150
MVC must satisfy a contract that produces a minimum of 100 Net models per week
MVC employs 25 workers, each of whom averages 30 production hours each per week
The following resources are available weekly:
Processors Hard Drives Other Drives
Celeron - 700 20 gb – 800 Floppy – 1600
Pentium - 550 30 gb – 950 Zip – 1000
Audiovisual Monitors Cases
CD / R/W – 1600 15” – 850 Mini – Tower – 1250
DVD – 900 17” – 800 Tower - 750
a. Determine the optimal weekly production schedule for MVC. What is the optimal weekly profit?
b. What is the minimum price that would justify producing the Plus model? Explain.
c. If MVC could purchase additional 17” monitors for $15 more than what they are currently paying for them, should they do this? Explain.
d. Suppose an additional worker could be hired for $1000 per week over the existing weekly worker salary. (Recall that workers average 30 hours per week.) Should MVC do this? Explain.
Develop a 2-3 page business Memorandum to detail your answers and recommendations
To determine the optimal weekly production schedule for MVC and calculate the optimal weekly profit, we need to perform linear programming. Here's how we can approach it:
Step 1: Define the Decision Variables:
Let x1, x2, x3, and x4 represent the number of Student, Plus, Net, and Pro models produced per week, respectively.
Step 2: Formulate the Objective Function:
The objective of MVC is to maximize profit. So, the objective function can be written as Z = 70x1 + 80x2 + 130x3 + 150x4.
Step 3: Formulate the Constraints:
a) To satisfy the contract, the production of Net models should be at least 100: x3 ≥ 100.
b) The total hours worked by 25 employees should not exceed 30 hours each, which gives a total of 750 hours: 0.4x1 + 0.5x2 + 0.6x3 + 0.8x4 ≤ 750.
Step 4: Add the Resource Availability Constraints:
For processors:
700Celeron + 550Pentium ≥ x1 + x2 + x3 + x4.
For hard drives:
800(20 gb) + 950(30 gb) ≥ x1 + x2 + x3 + x4.
For floppy drives:
1,600floppy drives ≥ x1 + x2 + 2x3 + x4.
For zip drives:
1,000zip drives ≥ x1 + x2 + x4.
For audio/visual:
1,600CD/RW + 900DVD ≥ x1 + x2 + x3 + x4.
For monitors:
850(15”) + 800(17”) ≥ x1 + x2 + x3 + x4.
For cases:
1,250mini-tower + 750tower ≥ x1 + x2 + x3 + x4.
Step 5: Solve the Linear Programming Problem:
Use any linear programming software or solver, such as Excel Solver or online linear programming tools, to solve the problem. Input the objective function and constraints, and the software will provide the optimal production quantities and the maximum profit.
To address the remaining questions (b, c, d), we'll need to review the results obtained from the linear programming solution.
b. To determine the minimum price that would justify producing the Plus model, we can calculate the shadow price for the Plus model in the linear programming solution. The shadow price represents the increase or decrease in profit for each unit change in the constraint.
c. Similarly, to decide if MVC should purchase additional 17” monitors, we'll need to calculate the shadow price for the monitors. If the shadow price is positive (greater than $15), it would justify the purchase.
d. For hiring an additional worker, we need to compare the increase in profit with the additional cost of $1000 per week. If the net increase in profit is higher than $1000, it would be beneficial to hire the additional worker.
By analyzing the obtained results and considering the costs and benefits involved in each scenario, we can provide recommendations and explanations in the business memorandum.