Question

Ina works in a juice firm and has to develop the production plan for the lemon and the orange juice concentrates. The fruits (lemon and orange) that she needs to make the juice are not the bottleneck but Ina is concerned about the other main ingredients that go into making the juice: a water-based solution, sugar, and a vitamin mix. Checking with the ERP system tells her that she has 10.3 metric tons of the water solution, 2.92 metric tons of sugar, and 2030 kg of vitamin mix. The recipe tells her to use 47 kg of water solution to make a metric ton of lemon drink and 72 kg of water solution to make a metric ton of orange drink. For the lemon drink she also needs 24 kg of sugar and 24 kg of vitamin mix. The orange drink needs 16 kg of sugar and 10 kg of vitamin mix.

From the sales department, Ina knows that the lemon soft drink sells at 60 SEK/metric ton and the orange drink sells at 75 SEK/metric ton. (SEK = Swedish krona).

How much lemon drink should Ina produce to maximize revenue?

Give your answer in metric tons and round to one decimal place.

How much orange drink should Ina produce to maximize revenue?

Give your answer in metric tons and round to one decimal.

How much revenue can Ina generate with the optimal production plan?

Round your answer to the nearest integer

Answer 1

This is a linear programming problem.

Given Information:

	Water Solution (kg)	Sugar (Kg)	Vitamin Mix (Kg)	Profit per kg
Constraints
Orange Mix	72	16	10	0.06 SEK
Lemon Mix	47	24	24	0.075 SEK
Availability	10300 kg	2920 kg	2030 kg

The linear programming can be formulated as follows:

Let the quantity of orange mix be x and lemon mix be y

Maximize Z = 0.06x + 0.075y

Subject to constraints:

72x + 47y < = 10300

16x + 24y <= 2920

10x + 24y <= 2030

x,y >= 0

The linear programming can be solved using excel:

Step 1: Put the data onto the spreadsheet

Step 2: The maximize function can be defined as follows:

Step 3: The water solution constraint can be defined as follows:

Step 4: The sugar constraint can be defined as follows:

Step 5: The vitamin mix constraint can be defined as follows:

Step 6: Go to data --> solver

Step 7: Now select the data and click solve

Production of lemon drink to maximize revenues: 0.0343 metric tonnes or 34.3 kg

Production of Orange drink to maximize revenues: 0.1206 metric tonnes or 120.6 kgs

Maximum Revenue = 9812.7 SEK per metric ton