Pets Plus, Inc. produces otic fluid for dogs. The otic fluid is sold in $12-$ounce plastic bottles. The sales budget for the first four months of the year is as follows:Assuming that the company is interested in maximizing the total profit contribution, answer the following:

$($a$)$ What is the linear programming model for this problem? If required, round your answers to $3$ decimal places or enter your answers as a fraction. If the

constant is $"1"$ it must be entered in the box. Do not round intermediate calculation. If an amount is zero, enter $"0".$

Let $R=$ number of units of regular model.

$C=$ number of units of catcher's model.