Return to sales The manufacturer of GRIPPER tires modeled its return to sales from television advertising expenditures in two regions, as follows. where S1 and S2 are the sales revenue in millions of dollars and x1 and x2 are millions of dollars of expenditures for television advertising. (a) What advertising expenditures would maximize sales revenue in each district? (b) How much money will be needed to maximize sales revenue in both districts?
Return to sales The manufacturer of GRIPPER tires modeled its return to sales from television advertising expenditures in two regions, as follows.
where S1 and S2 are the sales revenue in millions of dollars and x1 and x2 are millions of dollars of expenditures for television advertising.
(a) What advertising expenditures would maximize sales revenue in each district?
(b) How much money will be needed to maximize sales revenue in both districts?
Differentiating with respect to , we get
Differentiating with respect to , we get
a).
The maximum value of sales revenue occurs at which first derivative is zero. That is,
&
Hence,
Advertising expenditures of 25 million dollars would maximize sales revenue in region 1.
Advertising expenditures of 13.8461 million dollars would maximize sales revenue in region 2.
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