Chip Hoose is the owner of Hoose Custom Wheels. Chip has just received orders for 1,000 standard wheels and 1,250 deluxe wheels in month 1,800 standard and 1,500 deluxe for month 2, and 800 standard and 1,200 deluxe for month 3.  All orders must be filled. 

The cost of making standard wheels is $10 and deluxe wheels is $16. Overtime rates are 50% higher.  There are 1,000 hours of regular time and 500 hours of overtime available each month. It takes 0.5 hour to make a standard wheel and 0.6 hour to make a deluxe wheel.

The cost of storing a wheel from one month to the next is $2.

 

a. Formulate a linear programming model for this problem.

b. Solve the model by using Lingo.

For the very first month,

Total Number of hours required to make standard wheels = 0.5*1000 = 500 hours
Total Number of hours needed to make deluxe wheels = 0.6*1250 = 750 hours
As a result, we may divide this job into 1000 hours of regular time and 250 hours of overtime, and we can reduce costs by doing 750 hours of labor for deluxe wheels in normal time and the rest for standard.

Hence total cost for first month

1250*16 + 500*10 + 500*10*1.5 = 20,000 + 5000 + 7500

32500

Step-by-step explanation

For the very first month,

Total Number of hours required to make standard wheels = 0.5*1000 = 500 hours
Total Number of hours needed to make deluxe wheels = 0.6*1250 = 750 hours
As a result, we may divide this job into 1000 hours of regular time and 250 hours of overtime, and we can reduce costs by doing 750 hours of labor for deluxe wheels in normal time and the rest for standard.

Hence total cost for first month

1250*16 + 500*10 + 500*10*1.5 = 20,000 + 5000 + 7500

32500

Similarly, For the second month,

Total Number of hours required to make standard wheels = 0.5*800 = 400 hours
Total Number of hours required to make deluxe wheels = 0.6*1500 = 900 hours
As a result, we may divide this job into 1000 hours of regular time and 300 hours of overtime, and we can reduce costs by doing 900 hours of labor for deluxe wheels in regular time and the remainder for standard.

Hence total cost

1500*16 + 200*10 + 600*10*1.5 = 24,000 + 2000 + 9000

35000

For Third month,

Total Number of hours required to make standard wheels = 0.5*800 = 400 hours
Total Number of hours required to make deluxe wheels = 0.6*1200 = 720 hours
As a result, we may divide this job into 1000 hours of regular time and 120 hours of overtime, and we can reduce costs by doing 720 hours of work for deluxe wheels in regular time and the rest for standard.

Hence total cost

1200*16 + 560*10 + 240*10*1.5 = 19,200 + 5600 + 3600

28400