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kcwolford03
21.11.2019 •
Mathematics
Avegetable stand sells watermelons $5 each and honeydew melons for $3 each. one day they sold 6 more honeydew melons than watermelons,and their sales totaled $98.write andsolve a system of equations to find how many watermelons and honeydew melons they sold
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Ответ:
step-by-step explanation:
consider the statement as given in the text book,
let  be the number of acre of watermelon and  be the number of acre of cantaloupes.
number of salable units from each acre planted with watermelon is 90.
the selling price of a water melon is 
therefore, selling price of 90 watermelons is

total money that farmer will earn from  number of acres of watermelon is.
every acre of watermelon requires 20 pounds of fertilizer.
the cost price of 50-pound bag of fertilizer is 
cost price of 1-pound bag of fertilizer is 
cost price of 20-pound bag of fertilizer is

cost price of 20-pound bag of fertilizer for  be the acre of watermelon is 
the cost price of 1 hour of labor is 
the cost price of 2 hour of labor is

the cost price of 2 hour of labor is for  acre of watermelon is 
therefore, profit earned by farmer from watermelon is

number of salable units from each acre planted with cantaloupes is 300.
the selling price of cantaloupes is 
therefore, selling price of 300 cantaloupes is

total money that farmer will earn from  number of acres of cantaloupes is.
every acre of cantaloupes requires 15 pounds of fertilizer.
the cost price of 50-pound bag of fertilizer is 
cost price of 1-pound bag of fertilizer is 
cost price of 15-pound bag of fertilizer is

cost price of 15-pound bag of fertilizer for  be the acre of cantaloupes is 
the cost price of 1 hour of labor is 
the cost price of 2.5 hour of labor is

the cost price of 2.5 hour of labor is for  acre of cantaloupes is 
therefore, profit earned by farmer from cantaloupes is

the farmer wants to maximize their profit. therefore, the objective function for this model will be,
max: 
as farmer has 100-acre of farm with him. therefore,

as every acre planted with watermelon requires 50 gallons of water, so acre planted with watermelon will require  gallons of water.
as every acre planted with cantaloupes require 75 gallons of water, so acre planted with cantaloupes will require  gallons of water.
as farmer can pump about 6000 gallons of water, therefore

hence, the lp mode for this model is shown below,
max: 
subject to:

Ответ: