.AwholesalerofricebuyshergoodsfromTheRiceMasteratacostofGHS20forthe first200bags.Thispriceishoweverdecreasedby50pesewastimesthenumberof additionalbagsorderedabove200bags.Orderscannotbelessthan200units.The sellingpriceisafunctionofthenumberofbagsofriceorderedanditisgivenas p=22-0.01xwherexisthenumberofbagsofriceorderedinamonth. a.Whatnumberofunitsbeorderedtomaximiseprofit? b.Whatisthecorrespondingmaximumprofit? c.Ordersisrestrictedtoamaximumof4000bagsforonewholesaler,do youthinkitisworthorderingthemaximumnumberofbagsofrice?
Question
.AwholesalerofricebuyshergoodsfromTheRiceMasteratacostofGHS20forthe first200bags.Thispriceishoweverdecreasedby50pesewastimesthenumberof additionalbagsorderedabove200bags.Orderscannotbelessthan200units.The sellingpriceisafunctionofthenumberofbagsofriceorderedanditisgivenas p=22-0.01xwherexisthenumberofbagsofriceorderedinamonth. a.Whatnumberofunitsbeorderedtomaximiseprofit? b.Whatisthecorrespondingmaximumprofit? c.Ordersisrestrictedtoamaximumof4000bagsforonewholesaler,do youthinkitisworthorderingthemaximumnumberofbagsofrice?
Solution
a. To find the number of units to be ordered to maximise profit, we first need to find the cost function and the revenue function.
The cost function is given by: C(x) = 20200 + 0.50(x - 200) for x > 200 C(x) = 20200 for x <= 200
The revenue function is given by: R(x) = p*x = (22 - 0.01x)*x
The profit function is then given by the difference between the revenue and the cost: P(x) = R(x) - C(x)
To find the maximum profit, we need to find the derivative of the profit function and set it equal to zero, then solve for x.
b. To find the corresponding maximum profit, we substitute the value of x obtained in part a into the profit function P(x).
c. If the orders are restricted to a maximum of 4000 bags for one wholesaler, we need to evaluate the profit function at x = 4000 and compare it with the maximum profit obtained in part b. If the profit at x = 4000 is less than the maximum profit, then it is not worth ordering the maximum number of bags of rice. If the profit at x = 4000 is equal to or greater than the maximum profit, then it is worth ordering the maximum number of bags of rice.
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