A farmer has 10 acres to plant in corn and peas. He has to plant at least 7 acres. However, he has only $1200 to spend and each acre of corn costs $200 to plant and each acre of peas costs $100 to plant. Moreover, the farmer has to get the planting done in 12 hours and it takes an hour to plant an acre of corn and 2 hours to plant an acre of peas. If the profit is $500 per acre of corn and $300 per acre of peas how many acres of each should be planted to maximize profits? (a) Write three inequalities in x and y to represent the information given. (excluding the implied ?, ? ≥ 0) (b) Using a scale of 1cm to represent 1 unit on both axes, draw the graphs of the inequalities and shade the common region on the graph. (c) Using the profit values given above: (i). Write an expression to represent his total profit (ii). Use the graph to determine the values of x and y which gives a maximum profit, and hence determine the maximum profit
A farmer has 10 acres to plant in corn and peas. He has to plant at least 7 acres. However, he has only $1200 to
spend and each acre of corn costs $200 to plant and each acre of peas costs $100 to plant. Moreover, the farmer
has to get the planting done in 12 hours and it takes an hour to plant an acre of corn and 2 hours to plant an acre
of peas. If the profit is $500 per acre of corn and $300 per acre of peas how many acres of each should be
planted to maximize profits?
(a) Write three inequalities in x and y to represent the information given. (excluding the implied ?, ? ≥ 0)
(b) Using a scale of 1cm to represent 1 unit on both axes, draw the graphs of the inequalities and shade the
common region on the graph.
(c) Using the profit values given above:
(i). Write an expression to represent his total profit
(ii). Use the graph to determine the values of x and y which gives a maximum profit, and hence determine
the maximum profit
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