The Washington Apple Canning Company (WACCO) has purchased 3 000 000 kgs of apples of a...

  

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The Washington Apple Canning Company (WACCO) has purchased 3 000 000 kgs of apples of a total cost of $300 000 of which 20% was rated "A" quality and the remaining 80% was rated "B". WACCO's executives will soon meet to determine how to allocate the apples to three products, apple juice, apple sauce, and apple jelly, in a profit-optimal manner. The marketting department has estimated that WACCO could sell all the apple juice they could make, but that the demand for sauce and jelly was limited. Their demand forecasts are shown in Table 1. Table 2 shows the figures on price, cost, and profit per case of the apple products that were obtained from WACCO's accounting department. These figures include the cost of apples which was 5 cents per kilogram delivered to the cannery. The production manager indicated that it was impossible to produce only apple juice since too small a proportion of the crop was "A" quality. WACCO uses a numerical scale from 0 to 10 to rate the quality of both raw produce and prepared products, with the higher number representing higher quality. Grade A apples averaged 8 points per kg. whereas grade B apples averaged 4 points per kg. The minimum acceptable average quality requirement for apple juice had been set at 7, for apple sauce at 5, and for apple jelly at 4. You have been asked to come up not only with a recommendation for WACCO's executives, but also with an evaluation of the purchase of additional grade A apples as detailed below. 1. Formulate the problem of finding a profit-optimal allocation of grade A and B apples to the three apple products of WACCO as a linear programming model. 2. Compute the profit-optimal amount of grade A and B apples to be allocated to apple juice, sauce and jelly production using GAMS. Return your GAMS model with your answers. Product Apple juice Apple sauce Apple jelly Selling price per cane $ 3.18 $ 3.45 $ 3.05 Table 1: Selling price and demand forcast per case Product Selling price Variable cost Demand in cases Kg s per case 9 Direct Labor Variable Selling Packaging Material Apple Cost Total variable cost Profit 1 600 000 100 000 160 000 Apple juice Apple sauce $ 3.18 $ 3.45 $1.00 $ 0.25 $ 0.45 $ 0.90 $2.60 $ 0.58 Table 2: Product profit per case $ 1.13 $ 0.60 $ 0.40 $1.00 $ 3.13 $ 0.32 10 12.5 Appel jelly $3.05 $ 0.48 $ 0.22 $ 0.50 $ 1.25 $2.45 $ 0.60 The Washington Apple Canning Company (WACCO) has purchased 3 000 000 kgs of apples of a total cost of $300 000 of which 20% was rated "A" quality and the remaining 80% was rated "B". WACCO's executives will soon meet to determine how to allocate the apples to three products, apple juice, apple sauce, and apple jelly, in a profit-optimal manner. The marketting department has estimated that WACCO could sell all the apple juice they could make, but that the demand for sauce and jelly was limited. Their demand forecasts are shown in Table 1. Table 2 shows the figures on price, cost, and profit per case of the apple products that were obtained from WACCO's accounting department. These figures include the cost of apples which was 5 cents per kilogram delivered to the cannery. The production manager indicated that it was impossible to produce only apple juice since too small a proportion of the crop was "A" quality. WACCO uses a numerical scale from 0 to 10 to rate the quality of both raw produce and prepared products, with the higher number representing higher quality. Grade A apples averaged 8 points per kg. whereas grade B apples averaged 4 points per kg. The minimum acceptable average quality requirement for apple juice had been set at 7, for apple sauce at 5, and for apple jelly at 4. You have been asked to come up not only with a recommendation for WACCO's executives, but also with an evaluation of the purchase of additional grade A apples as detailed below. 1. Formulate the problem of finding a profit-optimal allocation of grade A and B apples to the three apple products of WACCO as a linear programming model. 2. Compute the profit-optimal amount of grade A and B apples to be allocated to apple juice, sauce and jelly production using GAMS. Return your GAMS model with your answers. Product Apple juice Apple sauce Apple jelly Selling price per cane $ 3.18 $ 3.45 $ 3.05 Table 1: Selling price and demand forcast per case Product Selling price Variable cost Demand in cases Kg s per case 9 Direct Labor Variable Selling Packaging Material Apple Cost Total variable cost Profit 1 600 000 100 000 160 000 Apple juice Apple sauce $ 3.18 $ 3.45 $1.00 $ 0.25 $ 0.45 $ 0.90 $2.60 $ 0.58 Table 2: Product profit per case $ 1.13 $ 0.60 $ 0.40 $1.00 $ 3.13 $ 0.32 10 12.5 Appel jelly $3.05 $ 0.48 $ 0.22 $ 0.50 $ 1.25 $2.45 $ 0.60