The maximum production of an oil refinery is 1400 barrels per day. The refinery can produce two types of fuel: gasoline and heating oil. The production cost per barrel if $6 for gasoline and $8 for heating oil. The daily production budget is $9600. The profit is $3 per barrel on gasoline and $4 per barrel on heating oil. What is the maximum total profit that can be realized daily

When a business is faced with a problem of shortage of a resource which can be used to produced more than one product type, to maximize the use of the resource , the business should allocate it for production purpose in such a way that it maximizes the contribution per unit of the scare resource.

Therefore the Company should allocate the budget cost to maximize the profit per production cost. This is done as follows:

Calculate the profit per budget cost and rank the product

Gasoline Heating oil

Profit per product cost 3/6=0.5 4/8= 0.5

The two products produce the same profit per dollar of cost which is $0.5. So, they are equally ranked.

So the total profit= the budget cost × profit per budget

= 9,600× $0.5 =$4,800

Maximum total profit = $4,800