A concert promoter produces two kinds of souvenir shirt, one kind sells for $18 ad the other for $25. The company determines, the total cost, in thous

Multivariable functions
asked 2021-01-05
A concert promoter produces two kinds of souvenir shirt, one kind sells for $18 ad the other for $25. The company determines, the total cost, in thousands of dollars, of producting x thousand of the $18 shirt and y thousand of the $25 shirt is given by
How many of each type of shirt must be produced and sold in order to maximize profit?

Answers (1)

Revenue function
Profit function
First we will find the critical point. Now,
And \(\displaystyle{P}_{{x}}{\left({x},{y}\right)}={0}\)
x=2 (i)
So, y=x+1
y=2 (ii)
Hence, the critical point is (2,3)
Since \(\displaystyle{f}_{{\times}},{f}_{{{y}{y}}},{\quad\text{and}\quad}{f}_{{{x}{y}}}\) all are constant so we will need to pkug critical point to function
Since, D>0, and \(\displaystyle{f}_{{\times}}{<}{0}\)</span>
The critical point P(2,3) has a relative maximum.
And the maximum value of profit function
The maximum profit of $19000 will be earned if 2000 shirt of $18 and 3000 shirts of $25 are produced and sold.
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