Acme Corporation has two factories that manufacture family-sized boxes of special vitamins for runners: Factory 1 has the capacity to produce 50 boxes per year, and Factory 2 has the capacity to produce 30 boxes per year. Four customers have already placed orders for the coming year: Wile E Coyote has ordered 20 boxes, Speedy Gonzalez has ordered 50 boxes, Sonic the Hedgehog has ordered 30 boxes, and Kid Flash has ordered 20 boxes. Acme’s management must decide how many boxes to supply to each customer. The customers are in different locations, so Acme can charge them different prices. However, differences in production and transportation costs mean that profits will not be maximised by selling to the highest bidder. The profits per box for each factory-customer combination are presented in Table 1. ACME TRIPLE-STRENGTH FORTIFIED LEG MUSCLE VITAMINS FAMILY SIZ (a) (4 marks) How many boxes of vitamins should each factory produce for each customer in order for Acme to maximise profits? (b) (2 marks) Which, if any, factories will have unused capacity in the coming year? (c) (2 marks) Which, if any, customer demands will not be met? (d) (2 marks) How much profit will Acme make? Table 1: Profits Per Box of Vitamins Kid Flash Wile E Coyote $32 $34 Speedy Gonzalez $36 $30 Sonic the Hedgehog $32 $28 Factory 1 Factory 2 $40 $38
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