Question

A vanilla cake requires $200\text{g}$ of flour and $25\text{g}$ of fat, and a strawberry cake requires $100\text{g}$ of flour and $50\text{g}$ of fat. From $5\text{kg}$ of flour and $1\text{kg}$ of fat, the maximum number of cakes that can be made is

• A. $45$
• B. $30$
• C. $25$
• D. $20$

Answer 1

The correct option is B $30$

Let $x$ number of vanilla cakes and $y$ number of strawberry cakes be made.
Then objective function is
Maximize $Z=x+y$
subject to constraints : maximum $5\text{kg}$ flour is available.
$\Rightarrow \frac{200}{1000}x+\frac{100}{1000}y\le 5$
$\Rightarrow 2x+y\le 50\cdots \left(i\right)$
and maximum $1\text{kg}$ of fat is available.
$\Rightarrow \frac{25}{1000}x+\frac{50}{1000}\le 1$
$\Rightarrow x+2y\le 40\cdots \left(ii\right)$
and $x,y\ge 0\cdots \left(iii\right)$
Now, plotting the graph of given constraints to get feasible region :


Now, tabulating the value of $Z=x+y$ at corner points :

Corner point : $(x,y)$	Value : $Z=x+y$
$(0,0)$	$0$
$(0,20)$	$20$
$(25,0)$	$25$
$(20,10)$	$30$ (maximum)

So, $Z_{max}=30$