Question

9) You are hired as a consulting engineer to a small gasoline refinery. You must determine how many gallons of three different grades of gasoline should be produced to maximize total profit. The gallons produced should not exceed the storage capacity of each grade. Also, there is a maximum of 16,500 eallons of raw oil available to produce the gasoline. The material requirements to produce one gallon of each grade are summarized in the table below (also in Excel). Max Storage Power Booster Production Hours Selling Raw Oil per 1000 Gallons Price (S/gal) Regular Mid-Grade Premiumm 1.3 1.45 1.55 $2.70 $2.90 $3.30 5000 4000 3500 1.5 1.2 1.4 2.1 Costs Power Production $1.48 50,27 $102.00 Max Raw Oil Available: 16,500 gallons

please explain steps to solution using excel

Answer 1

The answer has been presented in the supporting sheets. All the parts has been solved with detailed explanation and format. For detailed answers refer to the supporting sheets.

Answer Calculation of contribution margin per Raw oil gallon Regular Mid Grade Premium Selling Price Raw oil cost Power booster Production hours cost Contribution margin Raw oil per gallon Contribution margin per raw oil gallon (A/B) 2.7 1.924 0 0.102 0.674 1.3 2.9 2.146 0.405 0.1224 0.2266 1.45 3.3 2.294 0.567 0.1428 0.2962 1.55 0.5185 0.1563 0.1911 we will produce regular gasoline first then mid grade and then premium as contribution margin ratio per raw oil gallon is highest of regular then mid grade and then premium Statement of optimum product mix 5 Gasoline grade gallons producedRaw oil per gallon Total raw gasoline 6500 4575 5425 16500 Regular 1.3 1.45 1.55 5000 3155.17 3500 7 Mid grade Premium Total

Thus in order to maximise profit we need to produce Gasoline grade Regular Mid grade Premium gallons produced 5000 3155.17 3500 Notes 1. Firstly we have to prepare contribution margin statement for limiting factor that is raw gasoline olil 2. Then based on contribution margin per limiting factor we will decide which product is to be produced first. The product which highest contribution margin per limiting factor will be produced 3. then we prepare optimum product mix statement based on total limiting factor availability