Chapter 6.5, Problem 44S

(a)

To determine

To calculate: The inequality equation.

Answer to Problem 44S

The inequality equation is $115x+685y\ge 2300$ .

Explanation of Solution

Given information: The weekly overhead of shopkeeper is $2300, skimboards cost $115 each and longboards costs $685 each.

Calculation: The inequality equation will be,

  $\begin{array}{l}\text{Take}\text{number}\text{of}\text{skimboards}\text{as}x\text{and}\text{number}\text{of}\text{longboards}\text{as}y,\\ 115x+685y\ge 2300\end{array}$

(b)

To determine

To calculate: The minimum material that the shopkeeper attains profit.

Answer to Problem 44S

The number of sold skimboards is 1 and number of sold longboards is 4.

Explanation of Solution

Given information: The equation is given as,

  $115x+685y\ge 2300$

Calculation: The sold items will be,

  $\begin{array}{l}115x+685y\ge 2300\\ \text{Take}x=1,\\ 115\left(1\right)+685y\ge 2300\\ 685y\ge 2300-115\\ y\ge \frac{2185}{685}\\ y\text{must}\text{be}\text{an}\text{integer}\text{so,}\\ y=4\end{array}$

So the minimum number of skimboards to be sold is 1 and minimum number of longboards to be sold is 4.