Question Number 1151 by 123456 last updated on 05/Jul/15
$$\mathrm{what}\:\mathrm{the}\:\mathrm{min}\:\mathrm{value}\:\mathrm{of} \\ $$$$\mathrm{60}{x}+\mathrm{120}{y} \\ $$$$\mathrm{where} \\ $$$${x}+{y}=\mathrm{150} \\ $$$${x}\in\left\{\mathrm{0},\mathrm{1},...,\mathrm{150}\right\} \\ $$$${y}\in\left\{\mathrm{0},\mathrm{1},...,\mathrm{150}\right\} \\ $$
Answered by prakash jain last updated on 05/Jul/15
$${y}=\mathrm{150}−{x} \\ $$$$\mathrm{60}{x}+\mathrm{120}×\left(\mathrm{150}−{x}\right) \\ $$$$=\mathrm{120}×\mathrm{150}−\mathrm{60}{x} \\ $$$$\mathrm{min}\:\mathrm{value}\:\mathrm{at}\:{x}=\mathrm{150} \\ $$$$=\mathrm{18000}−\mathrm{9000}=\mathrm{9000} \\ $$