C&C is a meat processing facility that processes and packages meat products. It has recently negotiated a new delivery contract with a restaurant chain of four restaurants to deliver marinated vacuum sealed T$-$bone and rump steaks to the restaurant chain on a weekly basis. To bring down the cost of ready$-$mixed marinates, the management of C&C decided to mix their own marinate by combining three different secret spices, each containing certain amounts of five tenderising and flavouring agents. The marinate must be mixed in such a way that it contains adequate levels of tenderising and flavouring agents to ensure a tender product that is rich in flavour, but at the same time keeping the cost of the mix at a minimum. The following table shows these minimum requirements in units for each spice ingredients, as well as the cost of each of these spice ingredients:

In addition to this, it should be noted that only a limited amount of marinate mix can be prepared at any one time, as unused marinate mix will lose flavour during storage. Therefore, it is required that no more than a total of $160$ units should be contained in the prepared mix in order to limit the total prepared volume of marinate and thus prevent having to store of leftover marinate.

Develop the LP model $($showing all the relevant equations and inequalities$)$ required to determine the optimal mix of the secret spices that would minimize the cost of the marinate mix and solve this LP using a computer program.