Chapter 3.4, Problem 23PPS

To determine

To calculate: The number of yellow and strawberry cake to be produced to maximize the revenue.

Answer to Problem 23PPS

The number of yellow produced are 225 and strawberry cake are 0.

Explanation of Solution

Given information:

The cost of a yellow cake is $25 and that of strawberry cake is $35. It requires two hours to decorate and assemble a yellow cake and 3 hours for strawberry cake. The labor available for production is for 450 hours.

Calculation:

Consider the provided information that cost of a yellow cake is $25 and that of strawberry cake is $35. It requires two hours to decorate and assemble a yellow cake and 3 hours for strawberry cake. The labor available for production is for 450 hours.

Let x denote the number of yellow cake and y denote the number of strawberry cake.

Since, number of cakes produced cannot be negative so,

  $\begin{array}{c}x\ge 0\\ y\ge 0\end{array}$

The total number of working hours to produce the cakes are $2x+3y\le 450$.

Plot the inequalities and shade the common region $2x+3y\le 450,x\ge 0\text{ and }y\ge 0$

  

The profit function that is the revenue function that is to be maximized is $f\left(x,y\right)=25x+35y$.

Substitute the vertices of the feasible region to find the point at which maximum revenue is there.

Substitute $\left(0,0\right)$ in the function $f\left(x,y\right)=25x+35y$.

  $f\left(0,0\right)=0$

Substitute $\left(0,150\right)$ in the function $f\left(x,y\right)=25x+35y$.

  $f\left(0,150\right)=5250$

Substitute $\left(225,0\right)$ in the function $f\left(x,y\right)=25x+35y$.

  $f\left(225,0\right)=5625$

Since, maximum revenue is $5625 which is earned when yellow cakes produced are 225 and no strawberry cakes are produced.