### Problem 3A 28-inch-wide sheet of metal is to be bent into a rectangular trough with the cross-section shown in the diagram.#### Diagram Explanation:- The diagram depicts a rectangular trough's cross-section formed by bending a metal sheet.- The cross-section has: - **Depth (d)**: represented by the vertical dimension. - **Width (w)**: represented by the horizontal base of the trough.- The metal sheet's total width is labeled as **28 inches**.#### Task:Find the dimensions that will maximize the amount of water the trough can hold, i.e., find the dimensions that will maximize the cross-sectional area.#### Options:a. $ d = 7 \, \text{in.}, \, w = 21 \, \text{in.} $b. $ d = 7 \, \text{in.}, \, w = 14 \, \text{in.} $c. $ d = 7 \, \text{in.}, \, w = 7 \, \text{in.} $d. $ d = 5.6 \, \text{in.}, \, w = 11.2 \, \text{in.} $e. $ d = 14 \, \text{in.}, \, w = 14 \, \text{in.} $---### Problem 4A 270-room hotel is two-thirds filled when the nightly room rate is $100. Experience has shown that each $10 increase in cost results in 20 fewer occupied rooms. Find the nightly rate that will maximize income.#### Options:a. $45.00b. $285.00c. $185.00d. $150.00e. $200.00

Name: ### Problem 3A 28-inch-wide sheet of metal is to be bent into a recta
Uploaded: 2024-03-20T07:07:26.000Z
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Description: ### Problem 3A 28-inch-wide sheet of metal is to be bent into a rectangular trough with the cross-section shown in the diagram.#### Diagram Explanation:- The diagram depicts a rectangular trough's cross-section formed by bending a metal sheet.- The