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National Business Machines manufactures two models of fax machines: A and $B$. Each model A costs $$\$ 100$$ to make, and each model B costs $$\$ 150 .$$ The profit...

Question

National Business Machines manufactures two models of fax machines: A and $B$. Each model A costs $$\$ 100$$ to make, and each model B costs $$\$ 150 .$$ The profits are $$\$ 30$$ for each model $\mathrm{A}$ and $$\$ 40$$ for each model B fax machine. If the total number of fax machines demanded per month does not exceed 2500 and the company has earmarked no more than $$\$ 600,000 $$ month for manufacturing costs, how many units of each model should National make each month in order to maximize

National Business Machines manufactures two models of fax machines: A and $B$. Each model A costs $$\$ 100$$ to make, and each model B costs $$\$ 150 .$$ The profits are $$\$ 30$$ for each model $\mathrm{A}$ and $$\$ 40$$ for each model B fax machine. If the total number of fax machines demanded per month does not exceed 2500 and the company has earmarked no more than $$\$ 600,000 $$ month for manufacturing costs, how many units of each model should National make each month in order to maximize its monthly profit?



Answers

A merchant plans to sell two models of MP3 players at prices of $ \$225 $ and $ \$250 $. The $ \$225 $ model yields a profit of $ \$30 $ per unit and the $ \$250 $ model yields a profit of $ \$31 $ per unit. The merchant estimates that the total monthly demand will not exceed 275 units. The merchant does not want to invest more than $ \$63,000 $ in inventory for these products. What is the optimal inventory level for each model? What is the optimal profit?


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