Solving an Optimization Problem

I’m having difficulties solving an optimization problem. I have tried using linprog (https://se.mathworks.com/help/optim/ug/linprog.html), especially “Solve LP Using Problem-Based Approach for linprog”, however to no success. I suspect the ‘internal service/subassembly” of factor and might be the root of the problem.

I would like to obtain the Solution and Lagrange Multipliers as I need those to calculate marginal costs and graph these for different production mix of and .

I’m open to suggestions on how to solve this problem? Thanks!

The problem is given by:

Factor prices are given by , , , , and

A diagram of the production would look something like this:

Suppose and units are produced and the factor comsumptions are the solution to program.

The solution can be checked by the factor chocies are . This impies a total cost of 632.33.