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Question Number 32242 by pieroo last updated on 22/Mar/18

$$\mathrm{A}\mathrm{company}\mathrm{manufactures}\mathrm{two}\mathrm{types}\mathrm{of}\mathrm{products};$$$$\mathrm{X}(\mathrm{\$}4.50\mathrm{profit}\mathrm{per}\mathrm{item}\mathrm{x})\mathrm{and}\mathrm{Y}(\mathrm{\$}3.00\mathrm{profit}\mathrm{per}$$$$\mathrm{item}\mathrm{y}).\mathrm{These}\mathrm{items}\mathrm{are}\mathrm{built}\mathrm{using}\mathrm{both}\mathrm{machine}$$$$\mathrm{time}\mathrm{and}\mathrm{manual}\mathrm{labour}.\mathrm{The}\mathrm{X}\mathrm{product}\mathrm{requires}$$$$3\mathrm{hours}\mathrm{of}\mathrm{machine}\mathrm{time}\mathrm{and}\mathrm{two}\mathrm{hours}\mathrm{of}\mathrm{manual}$$$$\mathrm{labour}.\mathrm{The}\mathrm{Y}\mathrm{product}\mathrm{requires}3\mathrm{hours}\mathrm{of}\mathrm{machine}$$$$\mathrm{time}\mathrm{and}\mathrm{no}\mathrm{manual}\mathrm{labour}.\mathrm{If}\mathrm{the}{\mathrm{week}}^{\prime }\mathrm{s}\mathrm{supply}\mathrm{of}$$$$\mathrm{manual}\mathrm{labour}\mathrm{is}\mathrm{limited}\mathrm{to}8\mathrm{hours}\mathrm{and}\mathrm{machine}$$$$\mathrm{time}\mathrm{to}15\mathrm{hours},\mathrm{write}\mathrm{down}\mathrm{all}\mathrm{inequalities}$$$$\mathrm{involving}\mathrm{x}\mathrm{and}\mathrm{y}.$$

Answered by Joel578 last updated on 22/Mar/18

$$\{\begin{array}{l}3x+3y⩽15\\ 2x⩽8\\ x⩾0\\ y⩾0\end{array}$$

Commented by pieroo last updated on 22/Mar/18

$$\mathrm{thanks}\mathrm{very}\mathrm{much}$$

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