Question

you have 1000 available acres to plant grains and vegetables. the the table below the investment per acre for each crop, the expected produce harvested per acre and the revenue per crop unit are given. you wish to plant at least 50 acres of each of the five crops. your objective is to maximize profit.

investment/ acre	$20	$32	$23	$93	$81
expected crops/acre	45	48	23	31	43
revenue per crop unit	$1.79	$2.19	$2.89	$4.49	$2.59

please show me step by step how to figure out this and what constrants for solver

Answer 1

Let be the acres planted of each of the 5 crops respectively.

these are the decision variables.

The total investment to plant acres of each of these crops is

dollars

The expected total yield of each of the crops are units

The total revenue from all these 5 crops is

dollars

Hence the net profit from planing acres of these 5 crops is

We want to maximize this profit and hence this is the objective function

Finally the constraints

you have 1000 available acres to plant and hence the total area planted should not exceed 1000 acres.

you wish to plant at least 50 acres of each of the five crops , that is

We want to optimize the following LP model

Maximize

s.t

We now prepare the following sheet

get this sheet

set up the solver using data-->solver

get this

To maximize the profit, acres to be planted of each crop is

	Crop 1	Crop 2	Crop 3	Crop 4	Crop 5
Acres planted	50	800	50	50	50