Question
. 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
. 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. Coffee Blending Model: A coffee manufacturer blends three component coffee beans into three final blends of coffee. The Table below summarizes the very precise recipes for the final coffee blends, the cost and availability information for the three components, and the wholesale price per pound of the final blends. The percentages in the body of the table indicate the percentage of each component to be used in each blend.
Table: Percentage of each component to be used in each blend _____________________________________________________________________________ Final Blend (percent) Cost Per Maximum Availability Component 1 2 3 Pound Each Week (Pound) _____________________________________________________________________________ 1 80 0 20 $0.60 40,000 2 50 15 35 $0.80 25,000 3 0 40 60 $0.55 20,000 _____________________________________________________________________________ Wholesale Price/lb. $1.25 $1.50 $1.40 _____________________________________________________________________________ Weekly capacity for the processor's plant is 100,000 pounds, and the company wishes to operate at capacity. There is no problem in selling the final blends, although there is a requirement that minimum production level of 10,000, 25,000 and 30,000 pounds, respectively, be met for blends 1, 2 and 3. The manufacturer wishes to determine the number of pounds of each component which should be used in each blend so as to maximize total weekly profit. Formulate the problem as an L.P. model. Solve the model using a computer software and interpret the results.
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