11. The Pyrotec Company produces three electrical products-a locks, radios, and toasters. These products have the following resource requirements:

The manufacturer has a daily production budget of $2,000 and a maximum of 660 hours of labor, Maximum daily customer demand is for 200 clocks, 300 radios, and 150 toasters. Clocks sell for" $15, radios for $20, and toasters for $12. The company wants to know the Optimal product mix the-7; will maximize profit. . a. Formulate a linear programming model for this problem. I b. Solve the model by using the computer. ‘

40. The Valley Wine Company produces two kinds of wine-"Valley Nectar and Valley Red. The wines are produced from 64 tons of grapes the company has acquired this season. A LOGO—gallon batch of Nectar requires 4 tons of grapes, and a batch of Red requires 8 tons. However, production is limited by the availability of only 50 cubic yards of storage space for aging and 120 hours of processing time. A batch of each type of wine requires 5 yd.3 of storage space. The processing time for a batch of Nectar is 15 hours, and the processing time for a batch of Red is 8 hours. Demand for each type of wine is limited to seven batches. The profit for a batch of Nectar is $9,000, and the profit for a batch of Red is $12,000. The company wants to determine the number of 1,000-gallon batches of Nectar (x1) and Red (x2) to produce in order to maximize profit. a. Formulate a linear programming model for this problem. b. Solve this model by using graphical analysis.

1. The Ramon Company manufactures a wide range of products at several plant locations. The Franklin plant, which manufactures electrical components, has been experiencing difficulties with fluctuating monthly overhead costs. The fluctuations have made it difficult to estimate the level of overhead for any one month. Management wants to be able to estimate overhead costs accurately in order to better plan its operational and financial needs. A trade association publication to which Ramon Company subscribes indicates that for companies manufacturing electrical components, overhead tends to vary with direct labor-hours. Data on direct labor-hours and the respective overhead costs incurred have been collected for the past two (2) years. Below is the collected raw data.

1. Prepare a graph, including on it all data for the two-year period. Fit a regression line to the plotted points by visual inspection.
2. Using a linear regression method, determine the cost formula (Y = a + mx) for overhead in the Franklin plant.
3. What is the R2, for the overhead costs?
4. What is the reliability of this data?
5. Assume that the Franklin plant works 22,500 direct labor-hours during the month. Compute the expected overhead cost for the month.

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