Linear programming word problems

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  1. In a high school winter formal, male students are charged $20 per person and female students are charged $15 per person. The student association makes sure that the ratio between male and female is at least 1 to 3. Also, it is told by the school that the school hall can fit no more than 100 people. If the student association wants to maximize their profit, how many male and female students should there be in the winter formal?

    1. A toy factory produces dolls and robots. The factory indicates an expected demand of at least 90 dolls and 70 robots each day. Due to a shortage of raw materials, no more than 160 dolls and 155 robots can be produced daily. However, in order to honor the contract, at least 200 toys must be produced each day.

      If each doll sold results in a $2 loss whilst each robot sold generates a $4 profit, how many of each type should be produced daily in order to maximize profit?