Quantitative Math

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PROBLEM NO. 1

A manufacturer produces two models of racing bike, B and C, each of which must be processed through two machine shops. Machine shop 1 is available for 120 hours per month and machine shop 2 for 180 hours per month. The manufacture of each bike of type B takes 6 hours in shop 1 and 3 hours in shop 2. The corresponding times for C are 4 and 10 hours, respectively. If the profit is $180 and $220 per bike of type B and C respectively, how should the manufacturer arrange production to maximize total profit?

PROBLEM NO. 2

A small firm manufactures and sells liter cartons of non-alcoholic cocktails, ‘The Caribbean’ and ‘Mr. Fruity’, which sell for $1 and $1.25, respectively. Each is made by mixing fresh orange, pineapple and apple juices in different proportions. The Caribbean consists of 1 part orange, 6 parts pineapple and 1 part apple. Mr. Fruity consists of 2 parts orange, 3 parts pineapple and 1 part apple. The firm can buy up to 300 liters of orange juice, up to 1125 liters of pineapple juice and up to 195 liters of apple juice each week at a cost of $0.72, $0.64 and $0.48 per liter, respectively. Find the number of cartons of ‘The Caribbean’ and ‘Mr. Fruity’ that the firm should produce to maximize profits. You may assume that non-alcoholic cocktails are so popular that the firm can sell all that it produces.
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