Vita$-$Immune Ltd$.$ is considering expanding its product range by producing two new multivitamins and multi$-$minerals with Immunity booster ingredients in two different forms,

Gummies and Oral spray. Both products will be produced from the same resources but

with different combinations. These resources will be available to produce the new

products only. Details of estimated selling prices and cost per unit of each product are

given below:

Gummies Oral Spray

Selling Price per unit $229260$

Cost per unit:

Material A $(8$ per kg$)4016$

Material B $(20$ per kg$)2060$

Labour $(25$ per hour$)75100$

Variable overhead $(16$ per machine hour$)3248$

Total fixed costs are estimated to be $70,000$ per month. The management of VitaImmune Ltd$.$ Is in the process of using a linear programming model to determine the

optimal monthly production plan for the new products. The management accountant has

indicated that the following resources are available each month as follows:

Total monthly availability

Material A $10,150$ kg

Material B $5,500$ kg

Labour $8,400$ hours

Required:

$1.$ Formulate the objective function and constraints functions