Supertronic Ltd supplies each of four computer manufacturers (HP computers, ACCER computers, Apple computers and Dell computers) with a particular chip which can be produced in three different sizes such as 5 nanometers (nm) chip, 7 nanometers (nm) chip and 10 nanometers (nm) chip. Researchers say a new method of designing and building computer chips could lead to blisteringly quick processing of at least 1,000 times faster than the best existing chips are capable of. The manufacturing cost of the 5 nm chip amount to $50 per chips and it take two hours to manufacture. 

The manufacturing cost of the 7 nm chip is $40 per chips and the manufacturing time is 2½ hours. The 10 nm is manufactured specially for Apple computers, which has placed a permanent order of 7000 chips per week. The manufacturing cost is $100 per chips and it takes three hours to manufacture. A part from the permanent order for the 10 nm chip, there is no demand for this type. The marketing manager is certain that he will be able to sell as much 5 nm and 7 nm chips as can be produced, but at least 6000 chips of 5 nm chips must be produced per week so as to execute existing order.The production manager has consulted you to help him determine the weekly production of each type of chips, given an available factory capacity of 90 hours per week. 

REQUIRED: 

Formulate a linear programming model which is suitable for solving the problem by means of simplex method and solve it to find the optimal solution.